Abstract
We study Vasiliev’s system of higher spin gauge fields coupled to massive scalars in AdS 3, and compute the tree level two and three point functions. These are compared to the large N limit of the W N minimal model, and nontrivial agreements are found. We propose a modified version of the conjecture of Gaberdiel and Gopakumar, under which the bulk theory is perturbatively dual to a subsector of the CFT that closes on the sphere.
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J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
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].
A. Giveon, D. Kutasov and N. Seiberg, Comments on string theory on AdS 3, Adv. Theor. Math. Phys. 2 (1998) 733 [hep-th/9806194] [INSPIRE].
F. Larsen and E.J. Martinec, U(1) charges and moduli in the D1 - D5 system, JHEP 06 (1999) 019 [hep-th/9905064] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS 3 and SL(2, \( \mathbb{R} \)) WZW model 1.: The Spectrum, J. Math. Phys. 42 (2001) 2929 [hep-th/0001053] [INSPIRE].
I. Klebanov and A. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [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].
S. Giombi, S. Minwalla, S. Prakash, S. 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].
M.A. Vasiliev, More on equations of motion for interacting massless fields of all spins in (3 + 1)-dimensions, Phys. Lett. B 285 (1992) 225 [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories in four-dimensions, three-dimensions and two-dimensions, Int. J. Mod. Phys. D 5 (1996) 763 [hep-th/9611024] [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories: Star product and AdS space, hep-th/9910096 [INSPIRE].
M. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dS(d), Phys. Lett. B 567 (2003) 139 [hep-th/0304049] [INSPIRE].
M.A. Vasiliev, Higher spin algebras and quantization on the sphere and hyperboloid, Int. J. Mod. Phys. A 6 (1991) 1115 [INSPIRE].
M.R. Gaberdiel, R. Gopakumar and A. Saha, Quantum W-symmetry in AdS 3, JHEP 02 (2011) 004 [arXiv:1009.6087] [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].
C. Ahn, The large-N ’t Hooft Limit of Coset Minimal Models, JHEP 10 (2011) 125 [arXiv:1106.0351] [INSPIRE].
J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
M. Henneaux and S.-J. Rey, Nonlinear W infinity as asymptotic symmetry of three-dimensional higher spin Anti-de Sitter gravity, JHEP 12 (2010) 007 [arXiv:1008.4579] [INSPIRE].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, JHEP 11 (2010) 007 [arXiv:1008.4744] [INSPIRE].
M.R. Gaberdiel and T. Hartman, Symmetries of holographic minimal models, JHEP 05 (2011) 031 [arXiv:1101.2910] [INSPIRE].
E. Kiritsis and V. Niarchos, Large-N limits of 2d CFTs, Quivers and AdS 3 duals, JHEP 04 (2011) 113 [arXiv:1011.5900] [INSPIRE].
A. Castro, A. Lepage-Jutier and A. Maloney, Higher spin theories in AdS 3 and a gravitational exclusion principle, JHEP 01 (2011) 142 [arXiv:1012.0598] [INSPIRE].
E. Sezgin and P. Sundell, Analysis of higher spin field equations in four-dimensions, JHEP 07 (2002) 055 [hep-th/0205132] [INSPIRE].
E. Sezgin and P. Sundell, Holography in 4D (super) higher spin theories and a test via cubic scalar couplings, JHEP 07 (2005) 044 [hep-th/0305040] [INSPIRE].
A.C. Petkou, Evaluating the AdS dual of the critical O(N) vector model, JHEP 03 (2003) 049 [hep-th/0302063] [INSPIRE].
R.G. Leigh and A.C. Petkou, Holography of the N = 1 higher spin theory on AdS 4, JHEP 06 (2003) 011 [hep-th/0304217] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
S.S. Gubser and I.R. Klebanov, A universal result on central charges in the presence of double trace deformations, Nucl. Phys. B 656 (2003) 23 [hep-th/0212138] [INSPIRE].
S. Giombi and X. Yin, Higher spin gauge theory and holography: the three-point functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [INSPIRE].
S. Giombi and X. Yin, Higher spins in AdS and twistorial holography, JHEP 04 (2011) 086 [arXiv:1004.3736] [INSPIRE].
R. de Mello Koch, A. Jevicki, K. Jin and J.P. Rodrigues, AdS 4 /CFT 3 construction from collective fields, Phys. Rev. D 83 (2011) 025006 [arXiv:1008.0633] [INSPIRE].
M.R. Douglas, L. Mazzucato and S.S. Razamat, Holographic dual of free field theory, Phys. Rev. D 83 (2011) 071701 [arXiv:1011.4926] [INSPIRE].
K. Lang and W. Rühl, Anomalous dimensions of tensor fields of arbitrary rank for critical nonlinear O(N) σ-models at 2 < d < 4 to first order in 1/N, Z. Phys. C 51 (1991) 127 [INSPIRE].
K. Lang and W. Rühl, Field algebra for critical O(N) vector nonlinear σ-models at 2 < d < 4, Z. Phys. C 50 (1991) 285 [INSPIRE].
K. Lang and W. Rühl, The critical O(N) σ-model at dimension 2 < d < 4 and order 1/N 2 : operator product expansions and renormalization, Nucl. Phys. B 377 (1992) 371 [INSPIRE].
K. Lang and W. Rühl, The scalar ancestor of the energy momentum field in critical σ-models at 2 < d < 4, Phys. Lett. B 275 (1992) 93 [INSPIRE].
K. Lang and W. Rühl, The critical O(N) σ-model at dimensions 2 < d < 4: Fusion coefficients and anomalous dimensions, Nucl. Phys. B 400 (1993) 597 [INSPIRE].
F. Bais, P. Bouwknegt, M. Surridge and K. Schoutens, Extensions of the Virasoro Algebra Constructed from Kac-Moody Algebras Using Higher Order Casimir Invariants, Nucl. Phys. B 304 (1988) 348 [INSPIRE].
S. Giombi and X. Yin, On higher spin gauge theory and the critical O(N) model, Phys. Rev. D 85 (2012) 086005 [arXiv:1105.4011] [INSPIRE].
T. Banks and N. Seiberg, Symmetries and strings in field theory and gravity, Phys. Rev. D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].
S. Hellerman and E. Sharpe, Sums over topological sectors and quantization of Fayet-Iliopoulos parameters, Adv. Theor. Math. Phys. 15 (2011) 1141 [arXiv:1012.5999] [INSPIRE].
R. Metsaev, CFT adapted gauge invariant formulation of massive arbitrary spin fields in AdS, Phys. Lett. B 682 (2010) 455 [arXiv:0907.2207] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar, T. Hartman and S. Raju, Partition functions of holographic minimal models, JHEP 08 (2011) 077 [arXiv:1106.1897] [INSPIRE].
P. Bouwknegt and K. Schoutens, W symmetry in conformal field theory, Phys. Rept. 223 (1993) 183 [hep-th/9210010] [INSPIRE].
F. Bais, P. Bouwknegt, M. Surridge and K. Schoutens, Coset construction for extended Virasoro algebras, Nucl. Phys. B 304 (1988) 371 [INSPIRE].
T. Hartman and L. Rastelli, Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT, JHEP 01 (2008) 019 [hep-th/0602106] [INSPIRE].
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ArXiv ePrint: 1106.2580
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Chang, CM., Yin, X. Higher spin gravity with matter in AdS 3 and its CFT dual. J. High Energ. Phys. 2012, 24 (2012). https://doi.org/10.1007/JHEP10(2012)024
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DOI: https://doi.org/10.1007/JHEP10(2012)024