AdS-QCD correspondence




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 gravity-observables, for instance the shear viscosity of the quark-gluon plasma.

This perspective 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. 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 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)

    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

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 aply 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).

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.




  • 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)

  • 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)

  • 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)

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

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)

The Sakai-Sugimoto model 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

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

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 Zhou-Dosch 18

Application to hadron physics

Application to confined hadron-physics:


  • 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)

Original articles:

  • 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)

  • 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)

  • 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)

  • 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)

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)

Application to baryons as solitons/Skyrmions

Specifically application to baryon physics via Skyrmions and (equivalently) 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)

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

  • 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)

  • 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)

  • 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)

  • 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)

  • 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)

Application to glueball physics

  • 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:

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

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

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)

Last revised on May 18, 2019 at 14:37:47. See the history of this page for a list of all contributions to it.