Abstract
We study the AdS5/CFT4 duality where the boundary CFT is free Yang-Mills theory with gauge group SU(N). At the planar level we use the spectrum and correlation functions of the boundary theory to explicate features of the bulk theory. Further, by computing the one-loop partition function of the bulk theory using the methods of arXiv:1603.05387, we argue that the bulk coupling constant should be shifted to N 2 from N 2 − 1. Similar conclusions are reached by studying the dualities in thermal AdS5 with S 1 × S 3 boundary.
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References
G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
E. Sezgin and P. Sundell, Massless higher spins and holography, Nucl. Phys. B 644 (2002) 303 [Erratum ibid. B 660 (2003) 403] [hep-th/0205131] [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3 + 1)-dimensions, Phys. Lett. B 243 (1990) 378 [INSPIRE].
S.F. Prokushkin and M.A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3D AdS space-time, Nucl. Phys. B 545 (1999) 385 [hep-th/9806236] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, An AdS 3 dual for minimal model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].
M.A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dS(d), Phys. Lett. B 567 (2003) 139 [hep-th/0304049] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, D = 3 bosonic vector models coupled to Chern-Simons gauge theories, JHEP 03 (2012) 037 [arXiv:1110.4382] [INSPIRE].
S. Giombi, S. Minwalla, S. Prakash, S.P. Trivedi, S.R. Wadia and X. Yin, Chern-Simons theory with vector fermion matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].
S. Giombi and X. Yin, The higher spin/vector model duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].
S. Giombi, TASI lectures on the higher spin — CFT duality, arXiv:1607.02967 [INSPIRE].
S. Giombi and I.R. Klebanov, One loop tests of higher spin AdS/CFT, JHEP 12 (2013) 068 [arXiv:1308.2337] [INSPIRE].
S. Giombi, I.R. Klebanov and B.R. Safdi, Higher spin AdS d+1 /CFT d at one loop, Phys. Rev. D 89 (2014) 084004 [arXiv:1401.0825] [INSPIRE].
S. Giombi, I.R. Klebanov and A.A. Tseytlin, Partition functions and Casimir energies in higher spin AdS d+1 /CFT d , Phys. Rev. D 90 (2014) 024048 [arXiv:1402.5396] [INSPIRE].
M. Beccaria and A.A. Tseytlin, Higher spins in AdS 5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT, JHEP 11 (2014) 114 [arXiv:1410.3273] [INSPIRE].
M. Beccaria and A.A. Tseytlin, Vectorial AdS 5 /CFT 4 duality for spin-one boundary theory, J. Phys. A 47 (2014) 492001 [arXiv:1410.4457] [INSPIRE].
M. Beccaria, G. Macorini and A.A. Tseytlin, Supergravity one-loop corrections on AdS 7 and AdS 3 , higher spins and AdS/CFT, Nucl. Phys. B 892 (2015) 211 [arXiv:1412.0489] [INSPIRE].
M. Beccaria and A.A. Tseytlin, On higher spin partition functions, J. Phys. A 48 (2015) 275401 [arXiv:1503.08143] [INSPIRE].
M. Beccaria and A.A. Tseytlin, Iterating free-field AdS/CFT: higher spin partition function relations, J. Phys. A 49 (2016) 295401 [arXiv:1602.00948] [INSPIRE].
B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn-deconfinement phase transition in weakly coupled large-N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
M. Günaydin, D. Minic and M. Zagermann, 4D doubleton conformal theories, CPT and IIB string on AdS 5× S 5, Nucl. Phys. B 534 (1998) 96 [Erratum ibid. B 538 (1999) 531] [hep-th/9806042] [INSPIRE].
A. Barabanschikov, L. Grant, L.L. Huang and S. Raju, The spectrum of Yang-Mills on a sphere, JHEP 01 (2006) 160 [hep-th/0501063] [INSPIRE].
T.H. Newton and M. Spradlin, Quite a character: the spectrum of Yang-Mills on S 3, Phys. Lett. B 672 (2009) 382 [arXiv:0812.4693] [INSPIRE].
J.-B. Bae, E. Joung and S. Lal, One-loop test of free SU(N) adjoint model holography, JHEP 04 (2016) 061 [arXiv:1603.05387] [INSPIRE].
G. Mack, All unitary ray representations of the conformal group SU(2, 2) with positive energy, Commun. Math. Phys. 55 (1977) 1 [INSPIRE].
F.A. Dolan, Character formulae and partition functions in higher dimensional conformal field theory, J. Math. Phys. 47 (2006) 062303 [hep-th/0508031] [INSPIRE].
R. R. Metsaev, Massless mixed symmetry bosonic free fields in d-dimensional Anti-de Sitter space-time, Phys. Lett. B 354 (1995) 78.
R.R. Metsaev, Mixed symmetry massive fields in AdS 5, Class. Quant. Grav. 22 (2005) 2777 [hep-th/0412311] [INSPIRE].
R.R. Metsaev, Mixed-symmetry fields in AdS 5 , conformal fields and AdS/CFT, JHEP 01 (2015) 077 [arXiv:1410.7314] [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
D.E. Diaz and H. Dorn, Partition functions and double-trace deformations in AdS/CFT, JHEP 05 (2007) 046 [hep-th/0702163] [INSPIRE].
S. Giombi, A. Maloney and X. Yin, One-loop partition functions of 3D gravity, JHEP 08 (2008) 007 [arXiv:0804.1773] [INSPIRE].
J.R. David, M.R. Gaberdiel and R. Gopakumar, The heat kernel on AdS 3 and its applications, JHEP 04 (2010) 125 [arXiv:0911.5085] [INSPIRE].
R. Gopakumar, R.K. Gupta and S. Lal, The heat kernel on AdS, JHEP 11 (2011) 010 [arXiv:1103.3627] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar and A. Saha, Quantum W-symmetry in AdS 3, JHEP 02 (2011) 004 [arXiv:1009.6087] [INSPIRE].
R.K. Gupta and S. Lal, Partition functions for higher-spin theories in AdS, JHEP 07 (2012) 071 [arXiv:1205.1130] [INSPIRE].
D. Anselmi, Higher spin current multiplets in operator product expansions, Class. Quant. Grav. 17 (2000) 1383 [hep-th/9906167] [INSPIRE].
A.M. Polyakov, Gauge fields and space-time, Int. J. Mod. Phys. A 17S1 (2002) 119 [hep-th/0110196] [INSPIRE].
M. Bianchi, J.F. Morales and H. Samtleben, On stringy AdS 5 × S 5 and higher spin holography, JHEP 07 (2003) 062 [hep-th/0305052] [INSPIRE].
N. Beisert, M. Bianchi, J.F. Morales and H. Samtleben, On the spectrum of AdS/CFT beyond supergravity, JHEP 02 (2004) 001 [hep-th/0310292] [INSPIRE].
M. Spradlin and A. Volovich, A pendant for Polya: the one-loop partition function of N = 4 SYM on R × S 3, Nucl. Phys. B 711 (2005) 199 [hep-th/0408178] [INSPIRE].
M. Gunaydin, Singleton and doubleton supermultiplets of space-time supergroups and infinite spin superalgebras, in Trieste Conference on Supermembranes and Physics in 2 + 1 Dimensions, July 17–21, Trieste, Italy (1989).
E. Sezgin and P. Sundell, Towards massless higher spin extension of D = 5, N = 8 gauged supergravity, JHEP 09 (2001) 025 [hep-th/0107186] [INSPIRE].
E. Sezgin and P. Sundell, Doubletons and 5 − D higher spin gauge theory, JHEP 09 (2001) 036 [hep-th/0105001] [INSPIRE].
M.A. Vasiliev, Cubic interactions of bosonic higher spin gauge fields in AdS 5, Nucl. Phys. B 616 (2001) 106 [Erratum ibid. B 652 (2003) 407] [hep-th/0106200] [INSPIRE].
M.A. Vasiliev, Conformal higher spin symmetries of 4 − D massless supermultiplets and osp(L, 2M) invariant equations in generalized (super)space, Phys. Rev. D 66 (2002) 066006 [hep-th/0106149] [INSPIRE].
N. Beisert, M. Bianchi, J.F. Morales and H. Samtleben, Higher spin symmetry and N = 4 SYM, JHEP 07 (2004) 058 [hep-th/0405057] [INSPIRE].
M. Bianchi, P.J. Heslop and F. Riccioni, More on La Grande bouffe, JHEP 08 (2005) 088 [hep-th/0504156] [INSPIRE].
K.B. Alkalaev, O.V. Shaynkman and M.A. Vasiliev, On the frame-like formulation of mixed symmetry massless fields in (A)dS(d), Nucl. Phys. B 692 (2004) 363 [hep-th/0311164] [INSPIRE].
E.S. Fradkin and V. Ya. Linetsky, Conformal superalgebras of higher spins, Annals Phys. 198 (1990) 252 [INSPIRE].
X. Bekaert and M. Grigoriev, Manifestly conformal descriptions and higher symmetries of bosonic singletons, SIGMA 6 (2010) 038 [arXiv:0907.3195] [INSPIRE].
N. Boulanger and E.D. Skvortsov, Higher-spin algebras and cubic interactions for simple mixed-symmetry fields in AdS spacetime, JHEP 09 (2011) 063 [arXiv:1107.5028] [INSPIRE].
N. Boulanger, D. Ponomarev, E.D. Skvortsov and M. Taronna, On the uniqueness of higher-spin symmetries in AdS and CFT, Int. J. Mod. Phys. A 28 (2013) 1350162 [arXiv:1305.5180] [INSPIRE].
K. Govil and M. Günaydin, Deformed twistors and higher spin conformal (super-)algebras in four dimensions, JHEP 03 (2015) 026 [arXiv:1312.2907] [INSPIRE].
E. Joung and K. Mkrtchyan, Notes on higher-spin algebras: minimal representations and structure constants, JHEP 05 (2014) 103 [arXiv:1401.7977] [INSPIRE].
V. Alba and K. Diab, Constraining conformal field theories with a higher spin symmetry in D = 4, arXiv:1307.8092 [INSPIRE].
X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight, Towards holographic higher-spin interactions: four-point functions and higher-spin exchange, JHEP 03 (2015) 170 [arXiv:1412.0016] [INSPIRE].
X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight, Quartic AdS Interactions in higher-spin gravity from conformal field theory, JHEP 11 (2015) 149 [arXiv:1508.04292] [INSPIRE].
C. Sleight and M. Taronna, Higher spin interactions from conformal field theory: the complete cubic couplings, Phys. Rev. Lett. 116 (2016) 181602 [arXiv:1603.00022] [INSPIRE].
G.W. Gibbons, M.J. Perry and C.N. Pope, Partition functions, the Bekenstein bound and temperature inversion in Anti-de Sitter space and its conformal boundary, Phys. Rev. D 74 (2006) 084009 [hep-th/0606186] [INSPIRE].
S.H. Shenker and X. Yin, Vector models in the singlet sector at finite temperature, arXiv:1109.3519 [INSPIRE].
A. Jevicki, K. Jin and J. Yoon, 1/N and loop corrections in higher spin AdS 4 /CFT 3 duality, Phys. Rev. D 89 (2014) 085039 [arXiv:1401.3318] [INSPIRE].
G. Basar, A. Cherman, D.A. McGady and M. Yamazaki, Casimir energy of confining large-N gauge theories, Phys. Rev. Lett. 114 (2015) 251604 [arXiv:1408.3120] [INSPIRE].
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Bae, J.B., Joung, E. & Lal, S. On the holography of free Yang-Mills. J. High Energ. Phys. 2016, 74 (2016). https://doi.org/10.1007/JHEP10(2016)074
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DOI: https://doi.org/10.1007/JHEP10(2016)074