Contents

Idea

What is called holographic QCD or AdS/QCD correspondence or similar (review includes Aharony 02, Erlich 09, Kim-Yi 11, Erlich 14, Rebhan 14, Rho-Zahed 16) is a quantitatively predictive model for quantum chromodynamics (“QCD”, the strong nuclear force-sector of the standard model of particle physics) via “holography” (as in the AdS/CFT correspondence), hence regarding it as the boundary field theory of an (at least) 5-dimensional Yang-Mills theory (“bottom-up holographic QCD”), specifically one geometrically engineered on intersecting D-branes (“top-down holographic QCD”) and here specifically on D4-D8 brane intersections (the Witten-Sakai-Sugimoto model due to Witten 98, Karch-Katz 02, Sakai-Sugimoto 04, Sakai-Sugimoto 05).

While QCD, taken at face value, is not a quantum field theory of the kind considered in the plain AdS-CFT correspondence – since it is not a conformal field theory (but see KPV22) and not supersymmetric (hence not an SCFT, but see at hadron supersymmetry) and does not have a large number $N$ of colors (but see below), it is thought that approximations/deformations of AdS-CFT may still usefully apply.

Holographic QCD captures the non-perturbative confined regime of QCD, which is otherwise elusive (the Mass Gap Millennium Problem), where the would-be quarks are all bound/confined inside color-less hadrons, with the meson fields instead being the gauge field of a flavour-gauge theory (holographic dictionary, e.g. Kim-Yi 11 (3.1), see also “hidden local symmetry”) and the baryons being solitons of this flavour/meson field, namely skyrmions.

This dual description of the color gauge theory of quarks and gluons instead as flavour gauge theory of baryons and mesons is geometrically brought out by the D4-D8 brane intersections of the Witten-Sakai-Sugimoto intersecting D-brane model: Here the open strings on the D4 color branes give the color/gluon gauge field, while those on the D8 flavor branes give the flavour/meson gauge field, those stretching between D4 and D8 give the quarks and the closed strings give the glueballs. (See at WSS brane configuration below.) This way color/flavor duality is mapped to open/closed string duality (as the D8-branes are treated as probe branes).

Notice that the flavour sector is where most of the open problems regarding the standard model of particle physics are located (flavour problem, flavour anomalies).

Various fundamental characteristics of QCD that remain mysterious in the colored-quark model readily find a conceptual explanation in terms of this geometric engineering of flavour physics, notably the phenomena of confinement and of chiral symmetry breaking, but also for instance vector meson dominance and the Cheshire cat principle.

Indeed, holographic QCD gives accurate quantitative predictions of confined hadron spectra, hence of the physics of ordinary atomic nuclei (see comparison between experiment and predictions of holographic QCD below) which is out of reach for perturbation theory and otherwise computable, at best, via the blind numerics of lattice QCD. This means (Witten 98) that holographic QCD provides a conceptual solution to the mass gap problem (not yet a rigorous proof, but a proof strategy).

Concretely, much of the phenomenological success of holographic QCD is (review in Rho-Zahed 16, Chapter III) due to the holographic emergence of the time-honored but ad hoc Skyrmion-model of baryons, as solitons in the meson flavour-gauge field.

Moreover, in holographic QCD this Skyrmion model of baryons emerges in its modern improved form, where the pion field is accompanied by the whole tower of vector mesons (the rho meson etc.): these meson species are holographically unified as the transversal KK-modes in the holographic theory. Already just adjoining the rho meson to the pion makes the resulting Skyrmions, and hence holographic QCD, give accurate results for light nuclei all the way up to carbon (Naya-Sutcliffe 18a, Naya-Sutcliffe 18b).

The mechanism behind this description of baryons and nuclei via holographic QCD is the theorem of Atiyah-Manton 89 (highlighted as such in Sutcliffe 10) which identifies Skyrmions in 3+1-dimensional Yang-Mills theory with KK modes (transversal holonomies) of instantons in 4+1-dimensional YM theory:

This fact (of experiment/phenomenology on the left and of mathematics on the right) combined with the emergence of strings in the 't Hooft limit of QCD reveals a de facto holographic nature of QCD. The task in holographic QCD is to sort out the fine-print.

A key open problem here is that the AdS/CFT correspondence is currently well understood only in the large N limit, where the number $N_c$ of colors and the 't Hooft coupling $\lambda$ are both large. But for QCD the number of colors is small, $N_c = 3$. While the correspondence is thought to hold also in the small N limit, here the classical super-gravity-computations on the dual (AdS) side will receive small-N corrections (highlighted for holographic QCD e.g. in Sugimoto 16, see references below) from perturbative string theory (for small 't Hooft coupling) which are hard to compute, and then from M-theory (for small $N_c$) which are largely unknown, as formulating M-theory remains an open problem. Hence from the perspective of small-N corrected holographic QCD, the mass gap problem/confinement problem translates to the problem of formulating M-theory:

From Yi 09:

QCD is a challenging theory. Its most interesting aspects, namely the confinement of color and the chiral symmetry breaking, have defied all analytical approaches. While there are now many data accumulated from the lattice gauge theory, the methodology falls well short of giving us insights on how one may understand these phenomena analytically, nor does it give us a systematic way of obtaining a low energy theory of QCD below the confinement scale.

$[...]$

it has been proposed early on that baryons are topological solitons, namely Skyrmions $[$but$]$ the usual Skyrmion picture of the baryon has to be modified significantly in the context of full QCD.

$[...]$

the holographic picture naturally brings a gauge principle in the bulk description of the flavor dynamics in such a way that all spin one mesons as well as pions would enter the $[$ skyrmionic-$]$construction of baryons on the equal footing.

$[...]$

holographic QCD is similar to the chiral perturbation theory in the sense that we deal with exclusively gauge-invariant operators of the theory. The huge difference is, however, that this new approach tends to treat all gauge-invariant objects together. Not only the light meson fields like pions but also heavy vector mesons and baryons appear together, at least in principle. In other words, a holographic QCD deals with all color-singlets simultaneously, giving us a lot more predictive power.

$[...]$

The expectation that there exists a more intelligent theory consisting only of gauge-invariant objects in the large Nc limit is thus realized via string theory in a somewhat surprising manner that the master fields, those truly physical degrees of freedom, actually live not in four dimensional Minkowskian world but in five or higher dimensional curved geometry. This is not however completely unanticipated, and was heralded in the celebrated work by Eguchi and Kawai in early 1980’s which is all the more remarkable in retrospect.

$[...]$

To compare against actual QCD, we must fix $[$the 't Hooft coupling and the KK-scale$]$ to fit both the pion decay constant $f_\pi$ and the mass of the first vector meson. After this fitting, all other infinite number of masses and coupling constants are fixed. This version $[$the holographic WSS model$]$ of the holographic QCD is extremely predictive.

$[...]$

$[$this$]$ elevates the classic Skyrme picture based on pions to a unified model involving all spin one mesons in addition to pions. This is why the picture is extremely predictive.

As we saw in this note, for low momentum processes, such as soft pion processes, soft rho meson exchanges, and soft elastic scattering of photons, the $[$holographic WSS-$]$model’s predictions compare extremely well with experimental data. It is somewhat mysterious that the baryon sector works out almost as well as the meson sector

From Suganuma-Nakagawa-Matsumoto 16, p. 1:

Since 1973, quantum chromodynamics (QCD) has been established as the fundamental theory of the strong interaction. Nevertheless, it is very difficult to solve QCD directly in an analytical manner, and many effective models of QCD have been used instead of QCD, but most models cannot be derived from QCD and its connection to QCD is unclear.

To analyze nonperturbative QCD, the lattice QCD Monte Carlo simulation has been also used as a first-principle calculation of the strong interaction. However, it has several weak points. For example, the state information (e.g. the wave function) is severely limited, because lattice QCD is based on the path-integral formalism. Also, it is difficult to take the chiral limit, because zero-mass pions require infinite volume lattices. There appears a notorious “sign problem” at finite density.

On the other hand, holographic QCD has a direct connection to QCD, and can be derived from QCD in some limit. In fact, holographic QCD is equivalent to infrared QCD in large Nc and strong 't Hooft coupling $\lambda$, via gauge/gravity correspondence. Remarkably, holographic QCD is successful to reproduce many hadron phenomenology such as vector meson dominance, the KSRF relation, hidden local symmetry, the GSW model and the Skyrme soliton picture. Unlike lattice QCD simulations, holographic QCD is usually formulated in the chiral limit, and does not have the sign problem at finite density.

From Rho et a. 16:

One can make $[$chiral perturbation theory$]$ consistent with QCD by suitably matching the correlators of the effective theory to those of QCD at a scale near $\Lambda$. Clearly this procedure is not limited to only one set of vector mesons; in fact, one can readily generalize it to an infinite number of hidden gauge fields in an effective Lagrangian. In so doing, it turns out that a fifth dimension is “deconstructed” in a (4+1)-dimensional (or 5D) Yang–Mills type form. We will see in Part III that such a structure arises, top-down, in string theory.

$[...]$

$[$this holographic QCD$]$ model comes out to describe — unexpectedly well — low-energy properties of both mesons and baryons, in particular those properties reliably described in quenched lattice QCD simulations.

$[...]$

One of the most noticeable results of this holographic model is the first derivation of vector dominance (VD) that holds both for mesons and for baryons. It has been somewhat of an oddity and a puzzle that Sakurai's vector dominance — with the lowest vector mesons ρ and ω — which held very well for pionic form factors at low momentum transfers famously failed for nucleon form factors. In this holographic model, the VD comes out automatically for both the pion and the nucleon provided that the infinite $[$KK-$]$tower is included. While the VD for the pion with the infinite tower is not surprising given the successful Sakurai VD, that the VD holds also for the nucleons is highly nontrivial. $[...]$ It turns out to be a consequence of a holographic Cheshire Cat phenomenon

Models

In approaches to $AdS/QCD$ one distinguishes top-down model building – where the ambition is to first set up a globally consistent ambient intersecting D-brane model where a Yang-Mills theory at least similar to QCD arises on suitable D-branes (geometric engineering of gauge theories) – from bottom-up model building approaches which are more cavalier about global consistency and first focus on accurately fitting the intended phenomenology of QCD as the asymptotic boundary field theory of gravity+gauge theory on some anti de Sitter spacetime. (Eventually both these approaches should meet “in the middle” to produce a model which is both realistic as well as globally consistent as a string vacuum; see also at string phenomenology.)

graphics from Aldazabal-Ibáñez-Quevedo-Uranga 00

Top-down models

Witten-Sakai-Sugimoto model

A good top-down model building-approach to AdS/QCD is due to Sakai-Sugimoto 04, Sakai-Sugimoto 05 based on Witten 98, see Rebhan 14, Sugimoto 16 for review.

Brane configuration

The Witten-Sakai-Sugimoto model geometrically engineers something at least close to QCD: on the worldvolume of coincident black M5-branes with near horizon geometry a KK-compactification of $AdS_7 \times S^4$ in the decoupling limit where the worldvolume theory becomes the 6d (2,0)-superconformal SCFT. Here the KK-compactification is on a torus with anti-periodic boundary conditions for the fermions in one direction, thus breaking all supersymmetry (Scherk-Schwarz mechanism), where the first circle reduction realizes, under duality between M-theory and type IIA string theory, the M5-branes as D4-branes, hence the model now looks like 5d Yang-Mills theory further compactified on a circle. (Witten 98, section 4).

The further introduction of intersecting D8-branes and anti D8-branes to D4-D8 brane bound states makes a sensible sector of chiral fermions appear in this model (Sakai-Sugimoto 04, Sakai-Sugimoto 05)

The following diagram indicates the Witten-Sakai-Sugimoto intersecting D-brane model that geometrically engineers QCD:

graphics from Sati-Schreiber 19c

Here we are showing:

1. the color D4-branes;

2. the flavor D8-branes;

   with

   1. the 5d Chern-Simons theory on their worldvolume

   2. the corresponding 4d WZW model on the boundary

   exhibiting the vector meson fields in the Skyrmion model;

3. the baryon D4-branes

   (see below at Baryons);

4. the Yang-Mills monopole D6-branes

   (see at D6-D8-brane bound state);

5. the NS5-branes (often not considered here).

graphics from Sati-Schreiber 19c

Glueballs

Already before adding the D8-branes (hence already in the pure Witten model) this produces a pure Yang-Mills theory whose glueball-spectra may usefully be compared to those of QCD:

graphics from Rebhan 14

Hadrons

In this Witten-Sakai-Sugimoto model for strongly coupled QCD the hadrons in QCD correspond to string-theoretic-phenomena in the bulk field theory:

Mesons

The mesons (bound states of 2 quarks) correspond to open strings in the bulk, whose two endpoints on the asymptotic boundary correspond to the two quarks

Baryons

The baryons (bound states of $N_c$ quarks) appear in two different but equivalent (Sugimoto 16, 15.4.1) guises:

1. as wrapped D4-branes with $N_c$ open strings connecting them to the D8-brane

   (Witten 98b, Gross-Ooguri 98, Sec. 5, BISY 98, CGS98)

2. as skyrmions

   (Sakai-Sugimoto 04, section 5.2, Sakai-Sugimoto 05, section 3.3, see Bartolini 17).

For review see Sugimoto 16, Yi 09, Yi 11, Yi 13, also Rebhan 14, around (18).

graphics from Sugimoto 16

Equivalently, these baryon states are the Yang-Mills instantons on the D8-brane giving the D4-D8 brane bound state (Sakai-Sugimoto 04, 5.7) as a special case of the general situation for Dp-D(p+4)-brane bound states (e.g. Tong 05, 1.4).

graphics from Cai-Li 17

graphics from ABBCN 18

This already produces baryon mass spectra with moderate quantitative agreement with experiment (HSSY 07):

graphics from Sugimoto 16

Moreover, the above 4-brane model for baryons is claimed to be equivalent to the old Skyrmion model (see Sakai-Sugimoto 04, section 5.2, Sakai-Sugimoto 05, section 3.3, Sugimoto 16, 15.4.1, Bartolini 17).

But the Skyrmion model of baryons has been shown to apply also to bound states of baryons, namely the atomic nuclei (Riska 93, Battye-Manton-Sutcliffe 10, Manton 16, Naya-Sutcliffe 18), at least for small atomic number.

For instance, various experimentally observed resonances of the carbon nucleus are modeled well by a Skyrmion with atomic number 6 and hence baryon number 12 (Lau-Manton 14):

graphics form Lau-Manton 14

More generally, the Skyrmion-model of atomic nuclei gives good matches with experiment if not just the pi meson but also the rho meson-background is included (Naya-Sutcliffe 18):

graphics form Naya-Sutcliffe 18

WSS-type model for 2d QCD

There is a direct analogue for 2d QCD of the above WSS model for 4d QCD (Gao-Xu-Zeng 06, Yee-Zahed 11).

The corresponding intersecting D-brane model is much as that for 4d QCD above, just with

1. colorD2-branes instead of D4-branes;

2. baryon$\,$ D6-branes instead of D4-branes;

3. meson$\,$ fields given by 3d Chern-Simons theory instead of 5d Chern-Simons theory:

Type0B/$YM_4$-correspondence

Instead of starting with M5-branes in locally supersymmetric M-theory and then spontaneously breaking all supersymmetry by suitable KK-compactification as in the Witten-Sakai-Sugimoto model, one may start with a non-supersymmetric bulk string theory in the first place.

In this vein, it has been argued in GLMR 00 that there is holographic duality between type 0 string theory and non-supersymmetric 4d Yang-Mills theory (hence potentially something close to QCD). See also AAS 19.

Bottom-up models

A popular bottom-up approach of AdS/QCD is known as the hard-wall model (Erlich-Katz-Son-Stephanov 05).

Further refinement to the “soft-wall model” is due to KKSS 06 and further to “improved holographic QCD” is due to Gursoy-Kiritsis-Nitti 07, Gursoy-Kiritsis 08, see GKMMN 10.

Comparison with experiment

Comparison of holographic QCD models with experiment (mostly using bottom-up models).

Computations due to Katz-Lewandowski-Schwartz 05 using the hard-wall model (Erlich-Katz-Son-Stephanov 05) find the following comparison of AdS/QCD predictions to QCD-experiment

graphics from Erlich 09, section 1.2

Computations due to KKSS 06, Gursoy-Kiritsis-Nitti 07, Gursoy-Kiritsis 08, see GKMMN 10:

graphics from GKMMN 10

graphics from GKMMN 10

From Pomarol-Wulzer 09:

From da Rocha 21, for vector mesons:

for upsilon-mesons:

for psi-mesons:

for omega-mesons:

for phi-mesons:

Including the first heavy quarks:

From CLFH22:

On properties of the quark-gluon plasma in comparison to lattice QCD results:

Jokela, Järvinen & Piispa 2924:

“Holographic QCD has reached the level of sophistication that allows for a detailed reproduction of numerous lattice QCD outcomes”

NB: These computations so far all use just the field theory in the bulk, not yet the stringy modes (limit of vanishing string length $\sqrt{\alpha'} \to 0$). Incorporating bulk string corrections further improves these results, see Sonnenschein & Weissman 2018.

Embedding into the standard model of particle physics

Nastase 03, p. 2:

An obvious question then is can one lift this D brane construction for the holographic dual of QCD to a Standard Model embedding? I study this question in the context of D-brane-world GUT models and find that one needs to have TeV-scale string theory?.

Related concepts

• hadron supersymmetry, hadron Kaluza-Klein theory

• D=5 Yang-Mills theory

• confinement

  • chiral perturbation theory

  • quark bag model, Cheshire cat principle

  • Skyrmions

• lattice QCD

• AdS-CFT in condensed matter physics

• holographic Schwinger effect

• holographic entanglement entropy

• holography as Koszul duality

References

General

Review and introduction

Concerning the modern formulation of QCD via AdS/CFT duality:

• Ofer Aharony, The non-AdS/non-CFT correspondence, or three different paths to QCD, in: Progress in string, field and particle theory, Springer, (2003) 3-24 [arXiv:hep-th/0212193, doi:10.1007/978-94-010-0211-0]

• Stanley J. Brodsky, Guy F. de Teramond, AdS/CFT and Light-Front QCD, in: Search for the “Totally Unexpected” in the LHC Era, Proceedings of the International School of Subnuclear Physics, Erice 2007, World Scientific (2009) 139-176/183 [arXiv:0802.0514, doi:10.1142/7586, discussion: pdf]

• Hans Günter Dosch, A Practical Guide to AdS/CFT, lecture notes (2009) [pdf, pdf]

• Joshua Erlich, How Well Does AdS/QCD Describe QCD?, Int. J. Mod. Phys.A 25 (2010) 411-421 [arXiv:0908.0312, doi:10.1142/S0217751X10048718]

• Marco Panero, QCD thermodynamics in the large-$N$ limit, 2010 (PaneroAdsQCD.pdf)

• Youngman Kim, Deokhyun Yi, Holography at Work for Nuclear and Hadron Physics, Advances in High Energy Physics, Volume 2011, Article ID 259025, 62 pages (arXiv:1107.0155, doi:10.1155/2011/259025)

• Antoine Van Proeyen, Daniel Freedman, Chapter VIII of: Supergravity, Cambridge University Press (2012) [doi:10.1017/CBO9781139026833]

• Koji Hashimoto, §6.4 in: D-Brane – Superstrings and New Perspective of Our World, Springer (2012) [doi:10.1007/978-3-642-23574-0, spire:1188897]

• M. R. Pahlavani, R. Morad, Application of AdS/CFT in Nuclear Physics, Advances in High Energy Physics (arXiv:1403.2501)

• Jorge Casalderrey-Solana, Hong Liu, David Mateos, Krishna Rajagopal, Urs Achim Wiedemann, Gauge/string duality, hot QCD and heavy ion collisions, Cambridge University Press, 2014 (arXiv:1101.0618)

• Sinya Aoki, Koji Hashimoto, Norihiro Iizuka, Matrix Theory for Baryons: An Overview of Holographic QCD for Nuclear Physics, Reports on Progress in Physics, Volume 76, Number 10 (arxiv:1203.5386)

• Youngman Kim, Ik Jae Shin, Takuya Tsukioka, Holographic QCD: Past, Present, and Future, Progress in Particle and Nuclear Physics 68 (2013) 55-112 [arXiv:1205.4852]

• Joshua Erlich, An Introduction to Holographic QCD for Nonspecialists, Contemporary Physics, 56 2 (2015) [arXiv:1407.5002, doi:10.1080/00107514.2014.942079]

• Alberto Guijosa, QCD, with Strings Attached, IJMPE Vol. 25, No. 10 (2016) 1630006 [arXiv:1611.07472]

• Mannque Rho, Ismail Zahed (eds.) Part 4 “String Theory” of: The Multifaceted Skyrmion, World Scientific (2016) [doi:10.1142/9710]

• Sophia K Domokos, Robert Bell, Trinh La, Patrick Mazza, A Pedagogical Introduction to Holographic Hadrons, published as: Holographic hadron masses in the language of quantum mechanics, European Journal of Physics 42 6 (2021) 065801 [arXiv:2106.13136, doi:10.1088/1361-6404/ac1abb]

With emphasis on application to the QCD phase diagram and to the description of neutron stars:

• Matti Järvinen, Holographic modeling of nuclear matter and neutron stars, Eur. Phys. J. C. 56 (2021) [arXiv:2110.08281, doi:10.1140/epjc/s10052-022-10227-x]

• Niko Jokela, NICER view on holographic QCD, EPJ Web of Conferences 258 (2022) 07004 [arXiv:2111.07940, doi:10.1051/epjconf/202225807004]

See also:

• Wikipedia, AdS/QCD correspondence

Emphasis of the AdS-QCD correspondence at annual String-conferences:

• Igor Klebanov, Remarks on Color Confinement, talk at Strings 2021 (pdf, video)

• Sergei Dubovsky, Comments on (mostly long) QCD strings, talk at Strings 2021 (pdf, video)

• Nick Evans, Holography for Multi-Representation and Chiral Matter, talk at Strings 2022 [indico:4940848, slides, video]

  (emphasis on DBI action-effects)

• Umut Gürsoy, Recent developments in gauge-gravity duality applied to quantum many-body systems, talk at Strings 2022 [indico:4940863, pdf, video ]

• Edward Witten, Some Milestones in the Study of Confinement, talk at Prospects in Theoretical Physics 2023 – Understanding Confinement, IAS (2023) [web, YT]

40:13: “Personally, I think this setup really implies that pure $SU(N)$ gauge theory is dual to a string theory. The ‘only’ problem is that to get the pure gauge theory we need to make a relevant deformation and then take the limit that the deformation parameter is large…”

Top-down models

Witten-Sakai-Sugimoto model

Precursor developments:

• Tohru Eguchi, Hikaru Kawai, Reduction of Dynamical Degrees of Freedom in the Large-$N$ Gauge Theory, Phys. Rev. Lett. 48, 1063 (1982) (spire:176459, doi:10.1103/PhysRevLett.48.1063)

• Joseph Polchinski, Matthew Strassler, The String Dual of a Confining Four-Dimensional Gauge Theory (arXiv:hep-th/0003136)

  (discussion of confinement via AdS/CFT with a Myers effect in the bulk)

The top-down Sakai-Sugimoto model is due to

• Tadakatsu Sakai, Shigeki Sugimoto, Low energy hadron physics in holographic QCD, Progr. Theor. Phys. 113 (2005) 843-882 [arXiv:hep-th/0412141, doi:10.1143/PTP.113.843]

• Tadakatsu Sakai, Shigeki Sugimoto, More on a holographic dual of QCD, Progr. Theor. Phys. 114: 1083-1118, 2005 (arXiv:hep-th/0507073)

along the lines of

• Andreas Karch, Emanuel Katz, Adding flavor to AdS/CFT, JHEP 0206:043, 2002 (arxiv:hep-th/0205236)

and based on

• Edward Witten, Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge Theories, Adv. Theor. Math. Phys. 2 3 (1998) 505-532 [arXiv:hep-th/9803131, doi:10.4310/ATMP.1998.v2.n3.a3]

further developed in

• Lorenzo Bartolini, Stefano Bolognesi, Andrea Proto, From the Sakai-Sugimoto Model to the Generalized Skyrme Model, Phys. Rev. D 97, 014024 2018 (arXiv:1711.03873)

reviewed in:

• Piljin Yi, Topics in D4-D8 holographic QCD, 2009 (pdf slides)

• Shigeki Sugimoto, Holographic QCD – Status and perspectives, 2012 (pdf slides)

• Anton Rebhan, The Witten-Sakai-Sugimoto model: A brief review and some recent results, in Proceedings of: 3rd International Conference on New Frontiers in Physics, Kolymbari, Crete 2014, EPJ Web of Conferences

  95 02005 (2015) [arXiv:1410.8858, doi:10.1051/epjconf/20159502005]

• Mannque Rho, Ismail Zahed (eds.) The Multifaceted Skyrmion, World Scientific 2016 (doi:10.1142/9710)

• Si-wen Li, Xiao-tong Zhang, The D4/D8 model and holographic QCD [arXiv:2304.10826]

See also:

• Vikas Yadav, String/$\mathcal{M}$-theory Dual of Large-$N$ Thermal QCD-Like Theories at Intermediate Gauge/‘t Hooft Coupling and Holographic Phenomenology (arXiv:2111.12655)

More on D4-D8 brane bound states:

• Horatiu Nastase, Sections 2, 3 of: On Dp-Dp+4 systems, QCD dual and phenomenology (arXiv:hep-th/0305069)

The Witten-Sakai-Sugimoto model with orthogonal gauge groups realized by D4-D8 brane bound states at O-planes:

• Toshiya Imoto, Tadakatsu Sakai, Shigeki Sugimoto, $O(N)$ and $USp(N)$ QCD from String Theory, Prog.Theor.Phys.122:1433-1453, 2010 (arXiv:0907.2968)

• Hee-Cheol Kim, Sung-Soo Kim, Kimyeong Lee, 5-dim Superconformal Index with Enhanced $E_n$ Global Symmetry, JHEP 1210 (2012) 142 (arXiv:1206.6781)

Analogous discussion for flavour D6-branes:

• Jérôme Gaillard, On $G$-structures in gauge/string duality, 2011 (cronfa:42569 spire:1340775, pdf)

  (with emphasis of G-structures)

The analogoue of the WSS model for 2d QCD:

• Yi-hong Gao, Weishui Xu, Ding-fang Zeng, NGN, $QCD_2$ and chiral phase transition from string theory, Nucl.Phys. B400:181-210, 1993 (arXiv:hep-th/0605138)

Specifically concerning the 3d Chern-Simons theory on the D8-branes:

• Ho-Ung Yee, Ismail Zahed, Holographic two dimensional QCD and Chern-Simons term, JHEP 1107:033, 2011 (arXiv:1103.6286)

and its relation to baryons:

• Hideo Suganuma, Yuya Nakagawa, Kohei Matsumoto, 1+1 Large $N_c$ QCD and its Holographic Dual $\sim$ Soliton Picture of Baryons in Single-Flavor World, JPS Conf. Proc. 13, 020013 (2017) (arXiv:1610.02074)

On jet bundle cohomology in the Sakai-Sugimoto model:

• Ekkehart Winterroth, Variational cohomology and Chern-Simons gauge theories in higher dimensions (arXiv:2103.03037)

Comparison of the WSS model To lattice QCD:

• Nicolas Kovensky, Andreas Schmitt: Thermal pion condensation: holography meets lattice QCD [arXiv:2407.12641]

Further models

Variant with D4 flavor branes:

• Mark Van Raamsdonk, Kevin Whyte, Baryon charge from embedding topology and a continuous meson spectrum in a new holographic gauge theory, JHEP 1005:073, 2010 (arXiv:0912.0752)

• Shigenori Seki, Intersecting D4-branes Model of Holographic QCD and Tachyon Condensation, JHEP 1007:091, 2010 (arXiv:1003.2971)

See also:

• Nick Evans, Jack Mitchell, Domain Wall AdS/QCD, Phys. Rev. D 104 (2021) 094018 [arXiv:2108.12152, doi:10.1103/PhysRevD.104.094018]

• Nick Evans, Jack Mitchell, Thermal Transitions in Domain Wall AdS/QCD [arXiv:2207.10374]

Bottom-up models

Hard- and soft-wall model

The bottom-up hard-wall model is due to

• Joshua Erlich, Emanuel Katz, Dam T. Son, Mikhail A. Stephanov, QCD and a Holographic Model of Hadrons, Phys.Rev.Lett.95:261602, 2005 (arXiv:hep-ph/0501128)

while the soft-wall refinement is due to

• Andreas Karch, Emanuel Katz, Dam T. Son, Mikhail A. Stephanov, Linear Confinement and AdS/QCD, Phys.Rev.D74:015005, 2006 (arXiv:hep-ph/0602229)

reviewed in

• Sergey Afonin, Timofey Solomko, Motivations for the Soft Wall holographic approach to strong interactions [arXiv:2209.09042]

see also

• Alfredo Vega, Paulina Cabrera, Family of dilatons and metrics for AdS/QCD models, Phys. Rev. D 93, 114026 (2016) (arXiv:1601.05999)

• Alfonso Ballon-Bayona, Luis A. H. Mamani, Nonlinear realisation of chiral symmetry breaking in holographic soft wall models (arXiv:2002.00075)

and the version improved holographic QCD is due to

• Umut Gursoy, Elias Kiritsis, Exploring improved holographic theories for QCD: Part I, JHEP 0802:032, 2008 (arXiv:0707.1324)

• Umut Gursoy, Elias Kiritsis, Francesco Nitti, Exploring improved holographic theories for QCD: Part II, JHEP 0802:019, 2008 (arXiv:0707.1349)

reviewed in

• Umut Gürsoy, Elias Kiritsis, Liuba Mazzanti, Georgios Michalogiorgakis, Francesco Nitti, Improved Holographic QCD, Lect.Notes Phys.828:79-146,2011 (arXiv:1006.5461)

More developments on improved holographic QCD:

• Takaaki Ishii, Matti Järvinen, Govert Nijs, Cool baryon and quark matter in holographic QCD, J. High Energ. Phys. 2019 3 (2019) [doi:10.1007/JHEP07(2019)003, arXiv:1903.06169]

The extreme form of bottom-up holographic model building is explored in

• Koji Hashimoto, Sotaro Sugishita, Akinori Tanaka, Akio Tomiya, Deep Learning and Holographic QCD, Phys. Rev. D 98, 106014 (2018) (arXiv:1809.10536)

where an appropriate bulk geometry is computer-generated from specified boundary behaviour.

More on this:

• Tetsuya Akutagawa, Koji Hashimoto, Takayuki Sumimoto, Deep Learning and AdS/QCD (arXiv:2005.02636)

On the other hand, an embedding of the hard-wall model into type IIB string theory is discussed in:

• Akash Singh, K. P. Yogendran, Phases of a 10-D Holographic hard wall model [arXiv:2208.09387]

• Saulo Diles, On the spectrum of open strings in the Hard-Wall model of AdS/QCD: the role of $S^5$ [arXiv:2404.10183]

Holographic light-front QCD

The holographic formulation of light cone quantized QCD as holographic light front QCD:

Original articles:

• Stanley Brodsky, Guy de Teramond, Light-Front Hadron Dynamics and AdS/CFT Correspondence, Phys. Lett. B582:211-221, 2004 (arXiv:hep-th/0310227)

• Guy de Teramond, Stanley Brodsky, Light-Front Holography: A First Approximation to QCD, Phys. Rev. Lett. 102:081601, 2009 (arXiv:0809.4899)

Review in:

• Stanley Brodsky, Guy de Teramond, Hans Günter Dosch, Joshua Erlich,

  Light-Front Holographic QCD and Emerging Confinement, Physics Reports Volume 584, 8 July 2015, Pages 1-105 (arXiv:1407.8131)

• Liping Zou, Hans Günter Dosch, A very Practical Guide to Light Front Holographic QCD, (arXiv:1801.00607)

• Stanley Brodsky, Color Confinement and Supersymmetric Properties of Hadron Physics from Light-Front Holography, International Conference on Beauty, Charm and Hyperon Hadrons (BEACH 2018) 17–23 June 2018, Peniche, Portugal (arXiv:1912.12578)

• Ruben Sandapen, An overview of light-front holography (arXiv:2001.03479)

• Stanley Brodsky, Supersymmetric and Other Novel Features of Hadron Physics from Light-Front Holography, Proceedings of the 24th Workshop, “What Comes Beyond the Standard Models” (arXiv:2112.02453)

See also

• Harun Omer, Embedding LFHQCD in Worldsheet String Theory (arXiv:1909.12866)

Application to B-meson physics:

• Mohammad Ahmady, Holographic light-front QCD in B meson phenomenology (arXiv:2001.00266)

Relation to hadron supersymmetry

Discussion of hadron supersymmetry via light cone supersymmetric quantum mechanics in holographic light front QCD:

• Guy de Teramond, Hans Günter Dosch, Stanley Brodsky, Baryon Spectrum from Superconformal Quantum Mechanics and its Light-Front Holographic Embedding, Phys. Rev. D 91, 045040 (2015) (arXiv:1411.5243)

• Hans Günter Dosch, Guy de Teramond, Stanley Brodsky, Supersymmetry Across the Light and Heavy-Light Hadronic Spectrum, Phys. Rev. D 92, 074010 (2015) (arXiv:1504.05112)

• Stanley Brodsky, Guy de Téramond, Hans Günter Dosch, Cédric Lorcé, Meson/Baryon/Tetraquark Supersymmetry from Superconformal Algebra and Light-Front Holography, International Journal of Modern Physics AVol. 31, No. 19, 1630029 (2016) (arXiv:1606.04638)

• Hans Günter Dosch, Guy de Teramond, Stanley Brodsky, Supersymmetry Across the Light and Heavy-Light Hadronic Spectrum II, Phys. Rev. D 95, 034016 (2017) (arXiv:1612.02370)

• Marina Nielsen, Stanley Brodsky, Hadronic Superpartners from Superconformal and Supersymmetric Algebra, Phys. Rev. D 97, 114001 (2018) (arXiv:1802.09652)

• Marina Nielsen, Stanley Brodsky, Guy F. de Téramond, Hans Günter Dosch, Fernando S. Navarra, Liping Zou, Supersymmetry in the Double-Heavy Hadronic Spectrum, Phys. Rev. D 98, 034002 (2018) (arXiv:1805.11567)

String- and M-theory corrections

Generally on perturbative string theory-corrections (for small 't Hooft coupling $\lambda = g_{YM}^2 N$) and/or M-theory-corrections (small N) to the supergravity-approximation of the AdS/CFT correspondence, i.e. the small N corrections to the correspondence:

On the general need for M-theory at small $N_c$ in gauge/gravity duality:

• Leonard Susskind, Another Conjecture about M(atrix) Theory (arXiv:hep-th/9704080)

• Nissan Itzhaki, Juan Maldacena, Jacob Sonnenschein, Shimon Yankielowicz, Section 6 of: Supergravity and The Large $N$ Limit of Theories With Sixteen Supercharges, Phys. Rev. D 58, 046004 (1998) (arXiv:hep-th/9802042)

Discussion of small N effects in M-theory AdS4/CFT3 and using the conformal bootstrap:

• Nathan B. Agmon, Shai M. Chester, Silviu S. Pufu, Solving M-theory with the Conformal Bootstrap, JHEP 06 (2018) 159 (arXiv:1711.07343)

Specifically on small N corrections in holographic QCD:

• B. Basso, Cusp anomalous dimension in planar maximally supersymmetric Yang-Mills theory, Continuous Advances in QCD 2008, pp. 317-328 (2008) (spire:858223, doi:10.1142/9789812838667_0027)

  “The result $[$(29)$]$ coincides exactly with the recent two-loop stringy correction computed in Alday-Maldacena 07, providing a striking confirmation of the AdS/CFT correspondence.”

• H. Dorn, H.-J. Otto, On Wilson loops and $Q\bar Q$-potentials from the AdS/CFT relation at $T\geq 0$, In: Anna Ceresole, C. Kounnas , Dieter Lüst, Stefan Theisen (eds.) Quantum Aspects of Gauge Theories, Supersymmetry and Unification, Lecture Notes in Physics, vol 525. Springer 2007 (arXiv:hep-th/9812109, doi:10.1007/BFb0104268)

• Masayasu Harada, Shinya Matsuzaki, and Koichi Yamawaki, Implications of holographic QCD in chiral perturbation theory with hidden local symmetry, Phys. Rev. D 74, 076004 (2006) (doi:10.1103/PhysRevD.74.076004)

  (with an eye towards hidden local symmetry)

• Csaba Csaki, Matthew Reece, John Terning, The AdS/QCD Correspondence: Still Undelivered, JHEP 0905:067, 2009 (arXiv:0811.3001)

• Salvatore Baldino, Stefano Bolognesi, Sven Bjarke Gudnason, Deniz Koksal, A Solitonic Approach to Holographic Nuclear Physics, Phys. Rev. D 96, 034008 (2017) (arXiv:1703.08695)

• Vikas Yadav, Aalok Misra, On M-Theory Dual of Large-$N$ Thermal QCD-Like Theories up to $\mathcal{O}(R^4)$ and $G$-Structure Classification of Underlying Non-Supersymmetric Geometries (arXiv:2004.07259)

Hadron physics

Application to confined hadron-physics:

Review:

• Henrique Boschi-Filho, Hadrons in AdS/QCD models, Journal of Physics: Conference Series, Volume 706, Section 4 2008 (doi:10.1088/1742-6596/706/4/042008)

• Kanabu Nawa, Hideo Suganuma, Toru Kojo, Baryons in Holographic QCD, Phys.Rev.D75:086003, 2007 (arXiv:hep-th/0612187)

• Deog Ki Hong, Mannque Rho, Ho-Ung Yee, Piljin Yi, Chiral Dynamics of Baryons from String Theory, Phys. Rev. D76:061901, 2007 (arXiv:hep-th/0701276)

• Deog Ki Hong, Baryons in holographic QCD, talk at From Strings to Things 2008 (pdf)

• Johanna Erdmenger, Nick Evans, Ingo Kirsch, Ed Threlfall, Mesons in Gauge/Gravity Duals - A Review, Eur. Phys. J. A 35 (2008) 81-133 [arXiv:0711.4467, doi:10.1140/epja/i2007-10540-1]

• Stanley Brodsky, Hadron Spectroscopy and Dynamics from Light-Front Holography and Superconformal Algebra (arXiv:1802.08552)

• Koji Hashimoto, Tadakatsu Sakai, Shigeki Sugimoto, Holographic Baryons : Static Properties and Form Factors from Gauge/String Duality, Prog. Theor. Phys.120:1093-1137, 2008 (arXiv:0806.3122)

• Alex Pomarol, Andrea Wulzer, Baryon Physics in Holographic QCD, Nucl. Phys. B809:347-361, 2009 (arXiv:0807.0316)

• Thomas Gutsche, Valery E. Lyubovitskij, Ivan Schmidt, Alfredo Vega, Nuclear physics in soft-wall AdS/QCD: Deuteron electromagnetic form factors, Phys. Rev. D 91, 114001 (2015) (arXiv:1501.02738)

• Alex Pomarol, Andrea Wulzer, Baryon physics in a five-dimensional model of hadrons (arXiv:0904.2272), Chapter 18 in: Mannque Rho, Ismail Zahed (eds.) The Multifaceted Skyrmion, World Scientific 2016 (doi:10.1142/9710)

• Marco Claudio Traini, Generalized Parton Distributions: confining potential effects within AdS/QCD, Eur. Phys. J. C (2017) 77:246 (arXiv:1608.08410)

• Wenhe Cai, Si-wen Li, Holographic three flavor baryon in the Witten-Sakai-Sugimoto model with the D0-D4 background, Eur. Phys. J. C (2018) 78: 446 (arXiv:1712.06304)

• Valery E. Lyubovitskij, Ivan Schmidt, Gluon parton densities in soft-wall AdS/QCD (arXiv:2012.01334)

• Lorenzo Bartolini, Sven Bjarke Gudnason, Symmetry energy in holographic QCD [arXiv:2209.14309]

See also:

• Ruixiang Chen, Danning Li, Kazem Bitaghsir Fadafan, Mei Huang, The hadron spectra and pion form factor in dynamical holographic QCD model with anomalous 5D mass of scalar field [arXiv:2212.10363]

Baryons as instantons

baryons as instantons:

• Emanuel Katz, Adam Lewandowski, Matthew D. Schwartz, Phys. Rev. D74:086004, 2006 (arXiv:hep-ph/0510388)

• Hiroyuki Hata, Tadakatsu Sakai, Shigeki Sugimoto, Shinichiro Yamato, Baryons from instantons in holographic QCD, Prog.Theor.Phys.117:1157, 2007 (arXiv:hep-th/0701280)

• Hiroyuki Hata, Masaki Murata, Baryons and the Chern-Simons term in holographic QCD with three flavors (arXiv:0710.2579)

• Salvatore Baldino, Stefano Bolognesi, Sven Bjarke Gudnason, Deniz Koksal, A Solitonic Approach to Holographic Nuclear Physics, Phys. Rev. D 96, 034008 (2017) (arXiv:1703.08695)

• Chandan Mondal, Dipankar Chakrabarti, Xingbo Zhao, Deuteron transverse densities in holographic QCD, Eur. Phys. J. A 53, 106 (2017) (arXiv:1705.05808)

• Stanley J. Brodsky, Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra (arXiv:1709.01191)

• Alfredo Vega, M. A. Martin Contreras, Melting of scalar hadrons in an AdS/QCD model modified by a thermal dilaton (arXiv:1808.09096)

• Meng Lv, Danning Li, Song He, Pion condensation in a soft-wall AdS/QCD model (arXiv:1811.03828)

• Kazem Bitaghsir Fadafan, Farideh Kazemian, Andreas Schmitt, Towards a holographic quark-hadron continuity (arXiv:1811.08698)

• Jacob Sonnenschein, Dorin Weissman, Excited mesons, baryons, glueballs and tetraquarks: Predictions of the Holography Inspired Stringy Hadron model, (arXiv:1812.01619)

• Kazem Bitaghsir Fadafan, Farideh Kazemian, Andreas Schmitt, Towards a holographic quark-hadron continuity (arXiv:1811.08698)

• M. Abdolmaleki, G.R. Boroun, The Survey of Proton Structure Function with the AdS/QCD Correspondence Phys.Part.Nucl.Lett. 15 (2018) no.6, 581-584 (doi:10.1134/S154747711806002X)

• Si-wen Li, Hao-qian Li, Sen-kai Luo, Corrections to the instanton configuration as baryon in holographic QCD [arXiv:2209.12521]

• Si-wen Li, Hao-qian Li, Yi-peng Zhang: The worldvolume fermion as baryon in holographic QCD with instanton [arXiv:2402.01197]

On relation to type 0 string theory:

• Roberto Grena, Simone Lelli, Michele Maggiore, Anna Rissone, Confinement, asymptotic freedom and renormalons in type 0 string duals, JHEP 0007 (2000) 005 (arXiv:hep-th/0005213)

• Mohammad Akhond, Adi Armoni, Stefano Speziali, Phases of $U(N_c)$ $QCD_3$ from Type 0 Strings and Seiberg Duality (arxiv:1908.04324)

See also

• S. S. Afonin, AdS/QCD without Kaluza-Klein modes: Radial spectrum from higher dimensional QCD operators (arXiv:1905.13086)

In relation to the open string tachyon:

• Matti Järvinen, Elias Kiritsis, F. Nitti, E. Préau, Tachyon-dependent Chern-Simons terms and the V-QCD Baryon, J. High Energ. Phys. 2022 160 (2022) [doi:10.1007/JHEP12(2022)160, arXiv:2209.05868]

See also:

• Keiichiro Hori, Hideo Suganuma, Hiroki Kanda, Numerical analysis of a baryon and its dilatation modes in holographic QCD [arXiv:2307.16590]

Baryons as wrapped branes

baryons as wrapped D4-branes:

original articles:

• Edward Witten, Baryons And Branes In Anti de Sitter Space, JHEP 9807:006, 1998 (arXiv:hep-th/9805112)

• David Gross, Hirosi Ooguri, Aspects of Large $N$ Gauge Theory Dynamics as Seen by String Theory, Phys. Rev. D58:106002, 1998 (arXiv:hep-th/9805129)

• A. Brandhuber, N. Itzhaki, Jacob Sonnenschein, Shimon Yankielowicz, Baryons from Supergravity, JHEP 9807:020, 1998 (arxiv:hep-th/9806158)

• Yosuke Imamura, Supersymmetries and BPS Configurations on Anti-de Sitter Space, Nucl. Phys. B537:184-202, 1999 (arxiv:hep-th/9807179)

• Curtis Callan, Alberto Guijosa, Konstantin G. Savvidy, Baryons and String Creation from the Fivebrane Worldvolume Action (arxiv:hep-th/9810092)

• Curtis Callan, Alberto Guijosa, Konstantin G. Savvidy, Oyvind Tafjord, Baryons and Flux Tubes in Confining Gauge Theories from Brane Actions, Nucl. Phys. B555 (1999) 183-200 (arxiv:hep-th/9902197)

Review:

• Piljin Yi, Holographic Baryons (arXiv:0902.4515, doi:10.1142/9789814280709_0016), Chapter 16 in: Mannque Rho, Ismail Zahed (eds.) The Multifaceted Skyrmion, World Scientific 2016 (doi:10.1142/9710)

• Piljin Yi, Precision Holographic Baryons, AIP Conference Proceedings 1388, 106 (2011) (arXiv:1103.1684, doi:10.1063/1.3647358)

• Piljin Yi, Two Approaches to Holographic Baryons/Nuclei, Few-Body Syst (2013) 54: 77. (doi:10.1007/s00601-012-0373-7)

Baryons as Skyrmions

baryons as Skyrmions:

Review:

• Shigeki Sugimoto, Skyrmion and String theory, chapter 15 in Mannque Rho, Ismail Zahed (eds.) The Multifaceted Skyrmion, World Scientific 2016 (doi:10.1142/9710)

• Mannque Rho et al., Introduction to The Multifaceted Skyrmion, World Scientific 2016 (doi:10.1142/9710, pdf)

Original articles

• Kanabu Nawa, Hideo Suganuma, Toru Kojo, Brane-induced Skyrmions: Baryons in Holographic QCD, Prog.Theor.Phys.Suppl.168:231-236, 2007 (arXiv:hep-th/0701007)

• Hovhannes R. Grigoryan, Baryon as skyrmion-like soliton from the holographic dual model of QCD, talk at From Strings to Things 2008 (pdf)

• Paul Sutcliffe, Skyrmions, instantons and holography, JHEP 1008:019, 2010 (arXiv:1003.0023)

• Stefano Bolognesi, Paul Sutcliffe, The Sakai-Sugimoto soliton, JHEP 1401:078, 2014 (arXiv:1309.1396)

• Paul Sutcliffe, Holographic Skyrmions, Mod. Phys. Lett. B29 (2015) no. 16, 1540051 (spire:1383608)

Nucleons

nucleon form factors via holographic QCD:

• Kiminad A. Mamo, Ismail Zahed, Nucleon mass radii and distribution: Holographic QCD, Lattice QCD and GlueX data (arXiv:2103.03186)

• Roldão da Rocha, Information entropy of nuclear electromagnetic transitions in AdS/QCD [arXiv:2208.07191]

The derived parameters are shown to corroborate experimental data with great accuracy

via a nuclear matrix model:

• Koji Hashimoto, Norihiro Iizuka, Piljin Yi, A Matrix Model for Baryons and Nuclear Forces, JHEP 1010:003, 2010 (arXiv:1003.4988)

• Si-wen Li, Tuo Jia, Matrix model and Holographic Baryons in the D0-D4 background, Phys. Rev. D 92, 046007 (2015) (arXiv:1506.00068)

• Koji Hashimoto, Yoshinori Matsuo, Takeshi Morita, Nuclear states and spectra in holographic QCD, JHEP12 (2019) 001 (arXiv:1902.07444)

• Yasuhiro Hayashi, Takahiro Ogino, Tadakatsu Sakai, Shigeki Sugimoto, Stringy excited baryons in holographic QCD, Prog Theor Exp Phys (2020) (arXiv:2001.01461)

nuclear binding energy

• Salvatore Baldino, Lorenzo Bartolini, Stefano Bolognesi, Sven Bjarke Gudnason, Holographic Nuclear Physics with Massive Quarks (arXiv:2102.00680)

nuclear binding energy via the nuclear matrix model:

• Koji Hashimoto, Yoshinori Matsuo, Nuclear binding energy in holographic QCD (arXiv:2103.03563)

See also:

• Federico Castellani, Nucleon electric and magnetic polarizabilities in Holographic QCD [arXiv:2402.07553]

• Kazuo Ghoroku, Kouji Kashiwa, Yoshimasa Nakano, Motoi Tachibana, Fumihiko Toyoda: Chiral condensate in a holographic dilute nuclear matter [arXiv:2409.03268]

Pentaquarks

pentaquarks:

• Kazuo Ghoroku, Akihiro Nakamura, Tomoki Taminato, Fumihiko Toyoda, Holographic Penta and Hepta Quark State in Confining Gauge Theories, JHEP 1008:007,2010 (arxiv:1003.3698)

Parton distribution functions

• Matteo Rinaldi, Double parton correlations in mesons within AdS/QCD soft-wall models: a first comparison with lattice data (arXiv:2003.09400)

Flux string breaking

• Oleg Andreev, String Breaking, Baryons, Medium, and Gauge/String Duality (arXiv:2003.09880)

Glueball physics

• Kenji Suzuki, D0-D4 system and $QCD_{3+1}$, Phys.Rev. D63 (2001) 084011 (arXiv:hep-th/0001057)

• Alex S. Miranda, C. A. Ballon Bayona, Henrique Boschi-Filho, Nelson R. F. Braga, Glueballs at finite temperature from AdS/QCD, Nucl. Phys. Proc. Suppl. 199 (2010) 107-112 [arXiv:0910.4319, doi:10.1016/j.nuclphysbps.2010.02.013]

• S.S. Afonin, A.D. Katanaeva, Glueballs and deconfinement temperature in AdS/QCD (arXiv:1809.07730)

• S. S. Afonin, A. D. Katanaeva, E. V. Prokhvatilov, M. I. Vyazovsky, Deconfinement temperature in AdS/QCD from the spectrum of scalar glueballs (arXiv:2001.07990)

• Cornélio Rodrigues Filho, Glueballs in the Klebanov-Strassler Theory: Pseudoscalars vs Scalars (arXiv:2011.12689)

Application to vector meson dominance

Derivation of vector meson dominance via holographic QCD:

• D.T. Son, M.A. Stephanov, QCD and dimensional deconstruction, Phys. Rev. D69 (2004) 065020 (arXiv:hep-ph/0304182)

• Sungho Hong, Sukjin Yoon, Matthew Strassler, On the Couplings of Vector Mesons in AdS/QCD, JHEP 0604 (2006) 003 (arXiv:hep-th/0409118)

• Sungho Hong, Sukjin Yoon, Matthew Strassler, On the Couplings of the Rho Meson in AdS/QCD (cds:816440, arXiv:hep-ph/0501197)

• Leandro Da Rold, Alex Pomarol, Chiral symmetry breaking from five dimensional spaces, Nucl. Phys. B721:79-97, 2005 (arXiv:hep-ph/0501218)

and specifically in the Witten-Sakai-Sugimoto model:

• Tadakatsu Sakai, Shigeki Sugimoto, p. 18 and Section 5 of: More on a holographic dual of QCD, Progr. Theor. Phys. 114: 1083-1118, 2005 (arXiv:hep-th/0507073)

Application to the quark-gluon plasma

Application to the quark-gluon plasma:

Expositions and reviews include

• Pavel Kovtun, Quark-Gluon Plasma and String Theory, RHIC news (2009) (blog entry)

• Makoto Natsuume, String theory and quark-gluon plasma (arXiv:hep-ph/0701201)

• Steven Gubser, Using string theory to study the quark-gluon plasma: progress and perils (arXiv:0907.4808)

• Francesco Biagazzi, A. Cotrone, Holography and the quark-gluon plasma, AIP Conference Proceedings 1492, 307 (2012) (doi:10.1063/1.4763537, slides pdf)

• Brambilla et al., section 9.2.2 of QCD and strongly coupled gauge theories - challenges and perspectives, Eur Phys J C Part Fields. 2014; 74(10): 2981 (doi:10.1140/epjc/s10052-014-2981-5)

Holographic discussion of the shear viscosity of the quark-gluon plasma goes back to

• Giuseppe Policastro, D.T. Son, A.O. Starinets, Shear viscosity of strongly coupled $N=4$ supersymmetric Yang-Mills plasma, Phys. Rev. Lett.87:081601, 2001 (arXiv:hep-th/0104066)

Other original articles include:

• Brett McInnes, Holography of the Quark Matter Triple Point (arXiv:0910.4456)

• Hovhannes R. Grigoryan, Paul M. Hohler, Mikhail A. Stephanov, Towards the Gravity Dual of Quarkonium in the Strongly Coupled QCD Plasma (arXiv:1003.1138)

• Mansi Dhuria, Aalok Misra, Towards MQGP, JHEP 1311 (2013) 001 (arXiv:1306.4339)

• Irina Ya. Aref’eva, Kristina Rannu, Pavel Slepov, Energy Loss in Holographic Anisotropic Model for Heavy Quarks in External Magnetic Field (arXiv:2012.05758)

See also:

• Si-wen Li, Yi-peng Zhang, Correlation function of fundamental fermion in holographic QCD [arXiv:2307.13357]

• Nelson R. F. Braga, Octavio C. Junqueira, Hawking-Page transition in holographic QCD at finite density, Phys. Lett. B 855 (2024) 138813 [arXiv:2404.04683, doi:10.1016/j.physletb.2024.138813]

• Niko Jokela, Matti Järvinen, Aleksi Piispa, Refining holographic models of the quark-gluon plasma [arXiv:2405.02394]

  “Holographic QCD has reached the level of sophistication that allows for a detailed reproduction of numerous lattice QCD outcomes”

• Tuna Demircik, Niko Jokela, Matti Järvinen, Aleksi Piispa, Is holographic quark-gluon plasma homogeneous? [arXiv:2405.02392]

Application to lepton anomalous magnetic moment

Application to anomalous magnetic moment of the muon:

• Luigi Cappiello, What does Holographic QCD predict for anomalous $(g-2)_\mu$?, 2015 (pdf)

• Josef Leutgeb, Anton Rebhan, Axial vector transition form factors in holographic QCD and their contribution to the anomalous magnetic moment of the muon (arXiv:1912.01596)

• Josef Leutgeb, Anton Rebhan, Axial vector transition form factors in holographic QCD and their contribution to the muon $g-2$ (arXiv:2012.06514)

• Josef Leutgeb, Jonas Mager, Anton Rebhan, Holographic QCD and the muon anomalous magnetic moment (arXiv:2110.07458)

Application to the Higgs field

Application to the Higgs field:

• Domenec Espriu, Alisa Katanaeva, Composite Higgs Models: a new holographic approach (arXiv:1812.01523)

• Johanna Erdmenger, Nick Evans, Werner Porod, Konstantinos Rigatos, Gauge/gravity dual dynamics for the strongly coupled sector of composite Higgs models, JHEP 58 (2021) [arXiv:2010.10279, doi:10.1007/JHEP02(2021)058]

Application to $\theta$-angle axions and strong CP-problem

Realization of axions and solution of strong CP-problem:

• Francesco Bigazzi, Alessio Caddeo, Aldo L. Cotrone, Paolo Di Vecchia, Andrea Marzolla, The Holographic QCD Axion (arXiv:1906.12117)

Discussion of the theta angle via the the graviphoton in the higher WZW term of the D4-brane:

• Si-wen Li, around (3.1) of The theta-dependent Yang-Mills theory at finite temperature in a holographic description (arXiv:1907.10277)

Discussion of the Witten-Veneziano mechanism

• Josef Leutgeb, Anton Rebhan, Witten-Veneziano mechanism and pseudoscalar glueball-meson mixing in holographic QCD (arxiv:1909.12352)

See also:

• Si-wen Li, Hao-qian Li, Yi-peng Zhang, The worldvolume fermion as baryon in holographic QCD with a theta angle [arXiv:2402.01197]

Application to the QCD trace anomaly

Discussion of the QCD trace anomaly:

• Jose L. Goity, Roberto C. Trinchero, Holographic models and the QCD trace anomaly, Phys. Rev. D 86, 034033 – 2012 (arXiv:1204.6327)

• Aalok Misra, Charles Gale, The QCD Trace Anomaly at Strong Coupling from M-Theory (arXiv:1909.04062)

The QCD trace anomaly affects notably the equation of state of the quark-gluon plasma, see there at References – Holographic description of quark-gluon plasma

Application to parton distribution

• Akira Watanabe, Takahiro Sawada, Mei Huang, Extraction of gluon distributions from structure functions at small x in holographic QCD (arxiv:1910.10008)

Understanding the nucleon structure is one of the most important research topics in fundamental science, and tremendous efforts have been done to deepen our knowledge over several decades. $[...]$ Since $[these]$ are highly nonperturbative physical quantities, in principle they are not calculable by the direct use of QCD. Furthermore, although there is available data, this has large errors. These facts cause the huge uncertainties which can be seen in the preceding studies based on the global QCD analysis.

In this work, we investigate the gluon distribution in nuclei by calculating the structure functions in the framework of holographic QCD, which is constructed based on the AdS/CFT correspondence.

Application to QCD phases

Application to phases of QCD:

• R. Narayanan, H. Neuberger, A survey of large $N$ continuum phase transitions, PoSLAT 2007:020, 2007 (arXiv:0710.0098)

To colour superconductivity:

• Kazem Bitaghsir Fadafan, Jesus Cruz Rojas, Nick Evans, A Holographic Description of Colour Superconductivity, Phys. Rev. D 98 (2018) 066010 [arXiv:1803.03107, doi:10.1103/PhysRevD.98.066010]

to confinement/deconfinement phase transiton:

• Meng-Wei Li, Yi Yang, Pei-Hung Yuan Imprints of Early Universe on Gravitational Waves from First-Order Phase Transition in QCD (arXiv:1812.09676)

With magnetic fields:

• Umut Gursoy, Holographic QCD and magnetic fields (arXiv:2104.02839)

Of relevance in neutron stars:

• Carlos Hoyos, Niko Jokela, Matti Järvinen, Javier G. Subils, Javier Tarrio, Aleksi Vuorinen, Transport in strongly coupled quark matter, Phys. Rev. Lett. 125 (2020) 241601 7Lbrack;arXiv:2005.14205, doi:10.1103/PhysRevLett.125.241601]

• Carlos Hoyos, Niko Jokela, Matti Järvinen, Javier G. Subils, Javier Tarrio, Aleksi Vuorinen, Holographic approach to transport in dense QCD matter, Phys. Rev. D 105 6 (2022) 066014 [arXiv:2109.12122, doi:10.1103/PhysRevD.105.066014]

• Matti Järvinen, Holographic modeling of nuclear matter and neutron stars, Eur. Phys. J. C. 56 (2021) [arXiv:2110.08281, doi:10.1140/epjc/s10052-022-10227-x]

• Carlos Hoyos, Niko Jokela, Aleksi Vuorinen, Holographic approach to compact stars and their binary mergers, Prog. Part. Nucl. Phys. 126 (2022) 103972 [arXiv:2112.08422, doi:10.1016/j.ppnp.2022.103972]

See also

• Yosuke Imamura, Baryon Mass and Phase Transitions in Large N Gauge Theory, Prog. Theor. Phys. 100 (1998) 1263-1272 (arxiv:hep-th/9806162)

• Varun Sethi, A study of phases in two flavour holographic QCD (arXiv:1906.10932)

• Riccardo Argurio, Matteo Bertolini, Francesco Bigazzi, Aldo L. Cotrone, Pierluigi Niro, QCD domain walls, Chern-Simons theories and holography, J. High Energ. Phys. (2018) 2018: 90 (arXiv:1806.08292)

• Alfonso Ballon-Bayona, Jonathan P. Shock, Dimitrios Zoakos, Magnetic catalysis and the chiral condensate in holographic QCD (arXiv:2005.00500)

• Yi Yang, Pei-Hung Yuan, QCD Phase Diagram by Holography (arXiv:2011.11941)

• Nicolas Kovensky, Aaron Poole, Andreas Schmitt, Phases of cold holographic QCD: baryons, pions and rho mesons [arXiv:2302.10675]

• Jesús Cruz Rojas, Tuna Demircik, Matti Järvinen, Modulated instabilities and the $AdS_2$ point in dense holographic matter [arXiv:2405.02399]

Application to meson physics

Application to meson physics:

• Daniel Ávila, Leonardo Patiño, Melting holographic mesons by cooling a magnetized quark gluon plasma (arXiv:2002.02470)

• Xuanmin Cao, Hui Liu, Danning Li, Pion quasiparticles and QCD phase transitions at finite temperature and isospin density from holography, Phys. Rev. D 102, 126014 (2020) (arXiv:2009.00289)

• Xuanmin Cao, Songyu Qiu, Hui Liu, Danning Li, Thermal properties of light mesons from holography (arXiv:2102.10946)

• Daisuke Fujii, Akihiro Iwanaka, Mitsuru Tanaka: Gravitational form factors of pion from top-down holographic QCD [arXiv:2407.21113]

Application to quarkonium:

• Hovhannes R. Grigoryan, Paul M. Hohler, Mikhail A. Stephanov, Towards the Gravity Dual of Quarkonium in the Strongly Coupled QCD Plasma (arXiv:1003.1138)

• Rico Zöllner, Burkhard Kampfer, Holographic vector meson melting in a thermal gravity-dilaton background related to QCD (arXiv:2002.07200)

• Miguel Angel Martin Contreras, Saulo Diles, Alfredo Vega, Heavy quarkonia spectroscopy at zero and finite temperature in bottom-up AdS/QCD (arXiv:2101.06212)

Relation to holographic entanglement entropy

Relating to holographic entanglement entropy:

• Zhibin Li, Kun Xu, Mei Huang, The entanglement properties of holographic QCD model with a critical end point (arXiv:2002.08650)

Application to defects

Application to QCD with defects:

• Alexander Gorsky, Valentin Zakharov, Ariel Zhitnitsky, On Classification of QCD defects via holography, Phys. Rev. D79:106003, 2009 (arxiv:0902.1842)

Application to thermal QCD

Application to thermal QCD:

• Vikas Yadav, Aalok Misra, Towards Thermal QCD from M theory at Intermediate ‘t Hooft Coupling and G-Structure Classification of Non-supersymmetric Underlying Geometries (arXiv:2004.07259)

• Alfonso Ballon-Bayona, Luis A. H. Mamani, Alex S. Miranda, Vilson T. Zanchin, Effective holographic models for QCD: Thermodynamics and viscosity coefficients (arXiv:2103.14188)

• Qingxuan Fu, Song He, Li Li, Zhibin Li, Revisiting holographic model for thermal and dense QCD with a critical point [arXiv:2404.12109]

Application to anomalies

• Domingo Gallegos, Matti Järvinen, Eamonn Weitz, Chiral Separation Effect from Holographic QCD [arXiv:2406.07617]