AdS-QCD correspondence




The geometric engineering of quantum chromodynamics via D4-D8-brane bound state intersecting D-brane models is traditionally referred to as the AdS/QCD correspondence or as holographic QCD, or similar, referring to the use of the AdS/CFT correspondence. (Notice “CFT” as opposed to “QCD”).

The AdS-CFT correspondence applies exactly only to a few highly symmetric quantum field theories, notably to N=4 D=4 super Yang-Mills theory. However, away from these special points in field theory space the correspondence does not completely break down, but continues to apply in some approximation and/or with suitable modifications on the gravity-side of the correspondence.

Notably quantum chromodynamics (one sector of the standard model of particle physics) is crucially different from, but still similar enough to, N=4 D=4 super Yang-Mills theory that some of its observables, in particular otherwise intractable non-perturbative effects, have been argued to be usefully approximated by AdS-CFT-type dual supergravity-observables.

In particular, the realization of quantum chromodynamics by intersecting D-brane models gives a conceptual analytic handle on confined hadron spectra, hence of the physics of ordinary atomic nuclei (see below), which is otherwise computable only via the blind numerics of lattice QCD.

graphics grabbed from Aoki-Hashimoto-Iizuka 12

Other examples of such observables is the shear viscosity of the quark-gluon plasma.

This approach is hence called the AdS/QCD-correspondence or holographic QCD or similar (see also AdS-CFT in condensed matter physics for similar relations).


In approaches to AdS/QCDAdS/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 grabbed 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.

This model realizes something close to QCD on coincident black M5-branes with near horizon geometry a KK-compactification of AdS 7×S 4AdS_7 \times S^4 in the decoupling limit where the worldvolume theory becomes the 6d (2,0)-superconformal SCFT. 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).

This already produces a pure Yang-Mills theory whose glueball-spectra may usefully be compared to those of QCD:

graphics grabbed from Rebhan 14

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)

graphics grabbed from Erlich 09, section 1.1

graphics grabbed 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:

  1. 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

  2. baryons (bound states of N cN_c quarks) appear in two different but equivalent (Sugimoto 16, 15.4.1) guises:

    1. as wrapped D4-branes with N cN_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, also Rebhan 14, around (18).

graphics grabbed 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).

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

graphics grabbed 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 grabbed 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 grabbed form Naya-Sutcliffe 18

Type0B/YM 4YM_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).

Computations due to Katz-Lewandowski-Schwartz 05 find the following comparison of AdS/QCD predictions to QCD-experiment

graphics grabbed 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 grabbed from GKMMN 10

graphics grabbed from GKMMN 10

These computations shown so far all use just the field theory in the bulk, not yet the stringy modes (limit of vanishing string length α0\sqrt{\alpha'} \to 0). Incorporating bulk string corrections further improves these results, see Sonnenschein-Weissman 18.

Embedding into a full standard model

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?.




  • 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)

  • Youngman Kim and 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) -7+9 32

  • 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

The top-down Sakai-Sugimoto model is due to

based on

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

  • 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)

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:

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

see also

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

and the version improved holographic QCD is due to

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 (arXiv:1903.06169)

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 light-front holography approach is reviewed in

  • Liping Zou, H.G. Dosch, A very Practical Guide to Light Front Holographic QCD, (arXiv:1801.00607)

see also

Hadron physics

Application to confined hadron-physics:


  • 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)

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

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)

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)U(N_c) QCD 3QCD_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)

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

  • Curtis G. 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)


Baryons as Skyrmions

baryons as Skyrmions:


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)

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

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



  • 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)

Glueball physics

  • Kenji Suzuki, D0-D4 system and QCD 3+1QCD_{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)

Application to the quark-gluon plasma

Application to the quark-gluon plasma:

Expositions and reviews include

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 lepton anomalous magnetic moment

Application to anomalous magnetic moment of the muon:

  • Luigi Cappiello, What does Holographic QCD predict for anomalous (g2) μ(g-2)_\mu?, 2015 (pdf)

Application to Higgs field

Application to Higgs field:

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

Application to θ\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)

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 QCD phases

Application to phases of QCD

to colour superconductivity:

  • Kazem Bitaghsir Fadafan, Jesus Cruz Rojas, Nick Evans, A Holographic Description of Colour Superconductivity (arXiv:1803.03107)

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)

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)

Last revised on October 11, 2019 at 07:47:41. See the history of this page for a list of all contributions to it.