Abstract
We propose a duality between a higher spin \( \mathcal{N}=1 \) supergravity on AdS3 and a large N limit of a family of \( \mathcal{N}=\left( {1,1} \right) \) superconformal field theories. The gravity theory is an \( \mathcal{N}=1 \) truncation of the \( \mathcal{N}=2 \) supergravity found by Prokushkin and Vasiliev, and the dual conformal field theory is defined by a supersymmetric coset model. We check this conjecture by comparing one loop partition functions and find agreement. Moreover, we study the symmetry of the dual coset model and in particular compute fields of the coset algebra of dimension 3/2, 2, 2 and 5/2 explicitly.
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References
I. Klebanov and A. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [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.R. Gaberdiel and R. Gopakumar, Minimal model holography, arXiv:1207.6697 [INSPIRE].
C. Ahn, The large-N ’t Hooft limit of coset minimal models, JHEP 10 (2011) 125 [arXiv:1106.0351] [INSPIRE].
M.R. Gaberdiel and C. Vollenweider, Minimal model holography for SO(2N), JHEP 08 (2011) 104 [arXiv:1106.2634] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Ronne, Higher spin AdS 3 supergravity and its dual CFT, JHEP 02 (2012) 109 [arXiv:1111.2139] [INSPIRE].
S. 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].
P. Bouwknegt and K. Schoutens, W symmetry in conformal field theory, Phys. Rept. 223 (1993) 183 [hep-th/9210010] [INSPIRE].
M. Henneaux and S.-J. Rey, Nonlinear W ∞ 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].
A. Campoleoni, S. Fredenhagen and S. Pfenninger, Asymptotic W-symmetries in three-dimensional higher-spin gauge theories, JHEP 09 (2011) 113 [arXiv:1107.0290] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Triality in minimal model holography, JHEP 07 (2012) 127 [arXiv:1205.2472] [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].
C.-M. Chang and X. Yin, Higher spin gravity with matter in AdS 3 and its CFT dual, JHEP 10 (2012) 024 [arXiv:1106.2580] [INSPIRE].
K. Papadodimas and S. Raju, Correlation functions in holographic minimal models, Nucl. Phys. B 856 (2012) 607 [arXiv:1108.3077] [INSPIRE].
C. Ahn, The coset spin-4 Casimir operator and its three-point functions with scalars, JHEP 02 (2012) 027 [arXiv:1111.0091] [INSPIRE].
M. Ammon, P. Kraus and E. Perlmutter, Scalar fields and three-point functions in D = 3 higher spin gravity, JHEP 07 (2012) 113 [arXiv:1111.3926] [INSPIRE].
C.-M. Chang and X. Yin, Correlators in W N minimal model revisited, JHEP 10 (2012) 050 [arXiv:1112.5459] [INSPIRE].
C. Ahn, The primary spin-4 casimir operators in the holographic SO(N) coset minimal models, JHEP 05 (2012) 040 [arXiv:1202.0074] [INSPIRE].
Y. Kazama and H. Suzuki, New N = 2 superconformal field theories and superstring compactification, Nucl. Phys. B 321 (1989) 232 [INSPIRE].
Y. Kazama and H. Suzuki, Characterization of N = 2 superconformal models generated by coset space method, Phys. Lett. B 216 (1989) 112 [INSPIRE].
C. Candu and M.R. Gaberdiel, Supersymmetric holography on AdS 3, arXiv:1203.1939 [INSPIRE].
M. Henneaux, G. Lucena Gomez, J. Park and S.-J. Rey, Super-W ∞ asymptotic symmetry of higher-spin AdS 3 supergravity, JHEP 06 (2012) 037 [arXiv:1203.5152] [INSPIRE].
K. Hanaki and C. Peng, Symmetries of holographic super-minimal models, arXiv:1203.5768 [INSPIRE].
C. Ahn, The large-N ’t Hooft limit of Kazama-Suzuki model, JHEP 08 (2012) 047 [arXiv:1206.0054] [INSPIRE].
C. Candu and M.R. Gaberdiel, Duality in N = 2 minimal model holography, arXiv:1207.6646 [INSPIRE].
S. Fredenhagen, C. Restuccia and R. Sun, The limit of N = (2, 2) superconformal minimal models, JHEP 10 (2012) 141 [arXiv:1204.0446] [INSPIRE].
C. Ahn, The operator product expansion of the lowest higher spin current at finite N, JHEP 01 (2013) 041 [arXiv:1208.0058] [INSPIRE].
H. Tan, Exploring three-dimensional higher-spin supergravity based on sl(N|N − 1) Chern-Simons theories, JHEP 11 (2012) 063 [arXiv:1208.2277] [INSPIRE].
S. Datta and J.R. David, Supersymmetry of classical solutions in Chern-Simons higher spin supergravity, arXiv:1208.3921 [INSPIRE].
S. Fredenhagen and C. Restuccia, The geometry of the limit of N = 2 minimal models, J. Phys. A 46 (2013) 045402 [arXiv:1208.6136] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Ronne, Three point functions in higher spin AdS 3 supergravity, arXiv:1211.2237 [INSPIRE].
C. Candu, M.R. Gaberdiel, M. Kelm and C. Vollenweider, Even spin minimal model holography, arXiv:1211.3113 [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].
M.R. Gaberdiel, R. Gopakumar and A. Saha, Quantum W-symmetry in AdS 3, JHEP 02 (2011) 004 [arXiv:1009.6087] [INSPIRE].
L. Frappat, É. Ragoucy and P. Sorba, W algebras and superalgebras from constrained WZW models: a group theoretical classification, Commun. Math. Phys. 157 (1993) 499 [hep-th/9207102] [INSPIRE].
P. Di Francesco, P. Mathieu and D. Senechal, Conformal field theory, Springer, U.S.A. (1997).
D. Gepner, Field identification in coset conformal field theories, Phys. Lett. B 222 (1989) 207 [INSPIRE].
H. Weyl, The classical groups: their invariants and representations, Princeton University Press, Princeton U.S.A. (1939).
R.C. King, Branching rules for classical Lie groups using tensor and spinor methods, J. Phys. A 8 (1975) 429 [INSPIRE].
J. de Boer, L. Feher and A. Honecker, A class of W algebras with infinitely generated classical limit, Nucl. Phys. B 420 (1994) 409 [hep-th/9312049] [INSPIRE].
R. Blumenhagen, W. Eholzer, A. Honecker, K. Hornfeck and R. Hubel, Coset realization of unifying W algebras, Int. J. Mod. Phys. A 10 (1995) 2367 [hep-th/9406203] [INSPIRE].
E. Fradkin and V.Y. Linetsky, Supersymmetric Racah basis, family of infinite dimensional superalgebras, SU(∞ + 1|∞) and related 2D models, Mod. Phys. Lett. A 6 (1991) 617 [INSPIRE].
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ArXiv ePrint: 1209.5404
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Creutzig, T., Hikida, Y. & Rønne, P.B. \( \mathcal{N}=1 \) supersymmetric higher spin holography on AdS3 . J. High Energ. Phys. 2013, 19 (2013). https://doi.org/10.1007/JHEP02(2013)019
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DOI: https://doi.org/10.1007/JHEP02(2013)019