standard model of particle physics
matter field fermions (spinors, Dirac fields)
flavors of fundamental fermions in the standard model of particle physics: | |||
---|---|---|---|
generation of fermions | 1st generation | 2nd generation | 3d generation |
quarks ($q$) | |||
up-type | up quark ($u$) | charm quark ($c$) | top quark ($t$) |
down-type | down quark ($d$) | strange quark ($s$) | bottom quark ($b$) |
leptons | |||
charged | electron | muon | tauon |
neutral | electron neutrino | muon neutrino | tau neutrino |
bound states: | |||
mesons | light mesons: pion ($u d$) ρ-meson ($u d$) ω-meson ($u d$) f1-meson a1-meson | strange-mesons: ϕ-meson ($s \bar s$), kaon, K*-meson ($u s$, $d s$) eta-meson ($u u + d d + s s$) charmed heavy mesons: D-meson ($u c$, $d c$, $s c$) J/ψ-meson ($c \bar c$) | bottom heavy mesons: B-meson ($q b$) ϒ-meson ($b \bar b$) |
baryons | nucleons: proton $(u u d)$ neutron $(u d d)$ |
(also: antiparticles)
hadron (bound states of the above quarks)
minimally extended supersymmetric standard model
bosinos:
dark matter candidates
Exotica
general mechanisms
electric-magnetic duality, Montonen-Olive duality, geometric Langlands duality
string-fivebrane duality
string-QFT duality
QFT-QFT duality:
effective QFT incarnations of open/closed string duality,
relating (super-)gravity to (super-)Yang-Mills theory:
Seiberg duality (swapping NS5-branes)
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).
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
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
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.
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). Here 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
with
the 5d Chern-Simons theory on their worldvolume
the corresponding 4d WZW model on the boundary
exhibiting the vector meson fields in the Skyrmion model;
(see below at Baryons);
the Yang-Mills monopole D6-branes
(see at D6-D8-brane bound state);
the NS5-branes (often not considered here).
graphics from Sati-Schreiber 19c
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
In this Witten-Sakai-Sugimoto model for strongly coupled QCD the hadrons in QCD correspond to string-theoretic-phenomena in the bulk field theory:
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
The baryons (bound states of $N_c$ quarks) appear in two different but equivalent (Sugimoto 16, 15.4.1) guises:
as wrapped D4-branes with $N_c$ open strings connecting them to the D8-brane
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
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
meson$\,$ fields given by 3d Chern-Simons theory instead of 5d Chern-Simons theory:
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.
A popular bottom-up approach of AdS/QCD is known as the hard-wall model (Erlich-Katz-Son-Stephanov 05).
Computations due to Katz-Lewandowski-Schwartz 05 find the following comparison of AdS/QCD predictions to QCD-experiment
graphics from Erlich 09, section 1.2
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.
graphics from GKMMN 10
graphics from GKMMN 10
See also Pomarol-Wulzer 09:
These computations shown 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 18.
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?.
effective field theories of nuclear physics, hence for confined-phase quantum chromodynamics:
Ofer Aharony, The non-AdS/non-CFT correspondence, or three different paths to QCD, Progress in string, field and particle theory. Springer, Dordrecht, 2003. 3-24 (arXiv:hep-th/0212193)
Joshua Erlich, How Well Does AdS/QCD Describe QCD?, Int. J. Mod. Phys.A25:411-421,2010 (arXiv:0908.0312)
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)
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 Volume 68, January 2013, Pages 55-112 Progress in Particle and Nuclear Physics (arXiv:1205.4852)
Joshua Erlich, An Introduction to Holographic QCD for Nonspecialists, Contemporary Physics (arXiv:1407.5002)
Alberto Guijosa, QCD, with Strings Attached, IJMPE Vol. 25, No. 10 (2016) 1630006 (arXiv:1611.07472)
See also
Precursor developments:
The top-down Sakai-Sugimoto model is due to
Tadakatsu Sakai, Shigeki Sugimoto, Low energy hadron physics in holographic QCD, Progr. Theor. Phys. 113: 843-882, 2005 (arXiv:hep-th/0412141)
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
and based on
further developed in
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, 3rd International Conference on New Frontiers in Physics, Kolymbari, Crete, 2014 (arXiv:1410.8858)
Mannque Rho, Ismail Zahed (eds.) The Multifaceted Skyrmion, World Scientific 2016 (doi:10.1142/9710)
More on D4-D8 brane bound states:
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:
Specifically concerning the 3d Chern-Simons theory on the D8-branes:
and its relation to baryons:
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)
The bottom-up hard-wall model is due to
while the soft-wall refinement is due to
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
More developments on improved holographic QCD:
The extreme form of bottom-up holographic model building is explored in
where an appropriate bulk geometry is computer-generated from specified boundary behaviour.
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)
See also
Application to B-meson physics:
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)
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:
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)
The suggestion that the tower of observed vector mesons, when regarded as gauge fields of hidden local symmetries of chiral perturbation theory, is reasonably modeled as a Kaluza-Klein tower of D=5 Yang-Mills theory:
That the pure pion-Skyrmion-model of baryons is approximately the KK-reduction of instantons in D=5 Yang-Mills theory is already due to
with a hyperbolic space-variant in
The observation that the result of Atiyah-Manton 89 becomes an exact Kaluza-Klein construction of Skyrmions/baryons from D=5 instantons when the full KK-tower of vector mesons as in Son-Stephanov 03 is included into the Skyrmion model (see also there) is due to
Paul Sutcliffe, Skyrmions, instantons and holography, JHEP 1008:019, 2010 (arXiv:1003.0023)
Paul Sutcliffe, Holographic Skyrmions, Mod. Phys. Lett. B29 (2015) no. 16, 1540051 (spire:1383608, doi:10.1142/S0217984915400515)
In the Sakai-Sugimoto model of holographic QCD the D=5 Yang-Mills theory of this hadron Kaluza-Klein theory is identified with the worldvolume-theory of D8-flavour branes intersected with D4-branes in an intersecting D-brane model:
Tadakatsu Sakai, Shigeki Sugimoto, section 5.2 of Low energy hadron physics in holographic QCD, Prog.Theor.Phys.113:843-882, 2005 (arXiv:hep-th/0412141)
Tadakatsu Sakai, Shigeki Sugimoto, section 3.3. of More on a holographic dual of QCD, Prog.Theor.Phys.114:1083-1118, 2005 (arXiv:hep-th/0507073)
Hiroyuki Hata, Tadakatsu Sakai, Shigeki Sugimoto, Shinichiro Yamato, Baryons from instantons in holographic QCD, Prog.Theor.Phys.117:1157, 2007 (arXiv:hep-th/0701280)
Stefano Bolognesi, Paul Sutcliffe, The Sakai-Sugimoto soliton, JHEP 1401:078, 2014 (arXiv:1309.1396)
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)
Extensive review of this holographic/KK-theoretic-realization of quantum hadrodynamics from D=5 Yang-Mills theory is in:
Mannque Rho, Ismail Zahed (eds.) The Multifaceted Skyrmion, World Scientific, Second edition, 2016 (doi:10.1142/9710)
Via the realization of D4/D8 brane bound states as instantons in the D8-brane worldvolume-theory (see there and there), this relates also to the model of baryons as wrapped D4-branes, originally due to
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)
An alternative scenario of derivation of 4d Skyrmions by KK-compactification of D=5 Yang-Mills theory, now on a closed interval, motivated by M5-branes instead of by D4/D8-brane intersections as in the Sakai-Sugimoto model, is discussed in:
following
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. A35:81-133, 2008 (arXiv:0711.4467)
Stanley J. 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)
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)
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
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)
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)
Discussion of heavy flavor in holographic QCD:
Yizhuang Liu, Ismail Zahed, Heavy and Strange Holographic Baryons, Phys. Rev. D 96, 056027 (2017) (arXiv:1705.01397)
Si-wen Li, A holographic description of heavy-flavoured baryonic matter decay involving glueball, Phys. Rev. D 99, 046013 (2019) (arXiv:1812.03482)
(via additional flavor branes)
Nicolas Kovensky, Andreas Schmitt, Heavy Holographic QCD (arxiv:1911.08433)
Daisuke Fujii, Atsushi Hosaka, Heavy baryons in holographic QCD with higher dimensional degrees of freedom (arXiv:2003.13415)
(via higher KK-modes)
Kenji Suzuki, D0-D4 system and $QCD_{3+1}$, Phys.Rev. D63 (2001) 084011 (arXiv:hep-th/0001057)
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)
Interpretation in holographic QCD of the Schwinger effect of vacuum polarization as exhibited by the DBI-action on flavor branes:
Precursor computation in open string theory:
Relation to the DBI-action of a probe brane in AdS/CFT:
Gordon Semenoff, Konstantin Zarembo, Holographic Schwinger Effect, Phys. Rev. Lett. 107, 171601 (2011) (arXiv:1109.2920, doi:10.1103/PhysRevLett.107.171601)
S. Bolognesi, F. Kiefer, E. Rabinovici, Comments on Critical Electric and Magnetic Fields from Holography, J. High Energ. Phys. 2013, 174 (2013) (arXiv:1210.4170)
Yoshiki Sato, Kentaroh Yoshida, Holographic description of the Schwinger effect in electric and magnetic fields, J. High Energ. Phys. 2013, 111 (2013) (arXiv:1303.0112)
Yoshiki Sato, Kentaroh Yoshida, Holographic Schwinger effect in confining phase, JHEP 09 (2013) 134 (arXiv:1306.5512
Yoshiki Sato, Kentaroh Yoshida, Universal aspects of holographic Schwinger effect in general backgrounds, JHEP 12 (2013) 051 (arXiv:1309.4629)
Daisuke Kawai, Yoshiki Sato, Kentaroh Yoshida, The Schwinger pair production rate in confining theories via holography, Phys. Rev. D 89, 101901 (2014) (arXiv:1312.4341)
Yue Ding, Zi-qiang Zhang, Holographic Schwinger effect in a soft wall AdS/QCD model (arXiv:2009.06179)
Relation to DBI-action of flavor branes in holographic QCD:
Koji Hashimoto, Takashi Oka, Vacuum Instability in Electric Fields via AdS/CFT: Euler-Heisenberg Lagrangian and Planckian Thermalization, JHEP 10 (2013) 116 (arXiv:1307.7423)
Koji Hashimoto, Takashi Oka, Akihiko Sonoda, Magnetic instability in AdS/CFT: Schwinger effect and Euler-Heisenberg Lagrangian of Supersymmetric QCD, J. High Energ. Phys. 2014, 85 (2014) (arXiv:1403.6336)
Koji Hashimoto, Shunichiro Kinoshita, Keiju Murata, Takashi Oka, Electric Field Quench in AdS/CFT, J. High Energ. Phys. 2014 (arXiv:1407.0798)
Koji Hashimoto, Takashi Oka, Akihiko Sonoda, Electromagnetic instability in holographic QCD, J. High Energ. Phys. 2015, 1 (2015) (arXiv:1412.4254)
See also:
Xing Wu, Notes on holographic Schwinger effect, J. High Energ. Phys. 2015, 44 (2015) (arXiv:1507.03208, doi:10.1007/JHEP09(2015)044)
Kazuo Ghoroku, Masafumi Ishihara, Holographic Schwinger Effect and Chiral condensate in SYM Theory, J. High Energ. Phys. 2016, 11 (2016) (doi:10.1007/JHEP09(2016)011)
Le Zhang, De-Fu Hou, Jian Li, Holographic Schwinger effect with chemical potential at finite temperature, Eur. Phys. J. A54 (2018) no.6, 94 (spire:1677949, doi:10.1140/epja/i2018-12524-4)
Wenhe Cai, Kang-le Li, Si-wen Li, Electromagnetic instability and Schwinger effect in the Witten-Sakai-Sugimoto model with D0-D4 background, Eur. Phys. J. C 79, 904 (2019) (doi:10.1140/epjc/s10052-019-7404-1)
Zhou-Run Zhu, De-fu Hou, Xun Chen, Potential analysis of holographic Schwinger effect in the magnetized background (arXiv:1912.05806)
Zi-qiang Zhang, Xiangrong Zhu, De-fu Hou, Effect of gluon condensate on holographic Schwinger effect, Phys. Rev. D 101, 026017 (2020) (arXiv:2001.02321)
Review:
Daisuke Kawai, Yoshiki Sato, Kentaroh Yoshida, A holographic description of the Schwinger effect in a confining gauge theory, International Journal of Modern Physics A Vol. 30, No. 11, 1530026 (2015) (arXiv:1504.00459)
Akihiko Sonoda, Electromagnetic instability in AdS/CFT, 2016 (spire:1633963, pdf)
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:
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
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)
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)
Application to Higgs field:
Realization of axions and solution of strong CP-problem:
Discussion of the theta angle via the the graviphoton in the higher WZW term of the D4-brane:
Discussion of the Witten-Veneziano mechanism
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
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.
to confinement/deconfinement phase transiton:
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)
Application to meson physics:
Application to quarkonium:
Application of holographic QCD (holographic light front QCD) to B-meson physics and flavour anomalies:
Ruben Sandapen, Mohammad Ahmady, Predicting radiative B decays to vector mesons in holographic QCD (arXiv:1306.5352)
Mohammad Ahmady, R. Campbell, S. Lord, Ruben Sandapen, Predicting the $B \to \rho$ form factors using AdS/QCD Distribution Amplitudes for the $\rho$ meson, Phys. Rev. D88 (2013) 074031 (arXiv:1308.3694)
Mohammad Ahmady, Dan Hatfield, Sébastien Lord, Ruben Sandapen, Effect of $c \bar c$ resonances in the branching ratio and forward-backward asymmetry of the decay $B \to K^\ast\mu^+ \mu^-$
Mohammad Ahmady, Alexandre Leger, Zoe McIntyre, Alexander Morrison, Ruben Sandapen, Probing transition form factors in the rare $B \to K^\ast \nu \bar \nu$ decay, Phys. Rev. D 98, 053002 (2018) (arXiv:1805.02940)
Mohammad Ahmady, Holographic light-front QCD in B meson phenomenology, PoS DIS2013 (2013) 182 (arXiv:2001.00266)
Relating to holographic entanglement entropy:
Application to QCD with defects:
Last revised on May 29, 2020 at 03:01:44. See the history of this page for a list of all contributions to it.