Abstract
We propose a holographic duality between a higher spin AdS3 gravity with so(p) extended supersymmetry and a large N limit of a 2-dimensional Grassmannian-like model with a specific critical level k = N and a non-diagonal modular invariant. As evidence, we show the match of one-loop partition functions. Moreover, we construct symmetry generators of the coset model for low spins which are dual to gauge fields in the supergravity. Further, we discuss a possible relation to superstring theory by noticing an \( \mathcal{N}=3 \) supersymmetry of critical level model at finite k, N. In particular, we examine BPS states and marginal deformations. Inspired by the supergravity side, we also propose and test another large N CFT dual obtained as a \( {\mathrm{\mathbb{Z}}}_2 \) automorphism truncation of a similar coset model, but at a non-critical level.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
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.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, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [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].
C.-M. Chang, S. Minwalla, T. Sharma and X. Yin, ABJ triality: from higher spin fields to strings, J. Phys. A 46 (2013) 214009 [arXiv:1207.4485] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, \( \mathcal{N}=6 \) superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, \( \mathrm{Large}\hbox{-} \mathcal{N}=4 \) holography, JHEP 09 (2013) 036 [arXiv:1305.4181] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Rønne, Extended higher spin holography and Grassmannian models, JHEP 11 (2013) 038 [arXiv:1306.0466] [INSPIRE].
C. Ahn, Higher spin currents in Wolf space. Part I, JHEP 03 (2014) 091 [arXiv:1311.6205] [INSPIRE].
C. Candu and C. Vollenweider, On the coset duals of extended higher spin theories, JHEP 04 (2014) 145 [arXiv:1312.5240] [INSPIRE].
M.R. Gaberdiel and C. Peng, The symmetry of large \( \mathcal{N}=4 \) holography, JHEP 05 (2014) 152 [arXiv:1403.2396] [INSPIRE].
M. Beccaria, C. Candu and M.R. Gaberdiel, The \( \mathrm{large}\hbox{-} \mathcal{N}=4 \) superconformal W ∞ algebra, JHEP 06 (2014) 117 [arXiv:1404.1694] [INSPIRE].
Y. Kazama and H. Suzuki, Characterization of \( \mathcal{N}=2 \) superconformal models generated by coset space method, Phys. Lett. B 216 (1989) 112 [INSPIRE].
Y. Kazama and H. Suzuki, New \( \mathcal{N}=2 \) superconformal field theories and superstring compactification, Nucl. Phys. B 321 (1989) 232 [INSPIRE].
P. Spindel, A. Sevrin, W. Troost and A. Van Proeyen, Extended supersymmetric σ-models on group manifolds. 1. The complex structures, Nucl. Phys. B 308 (1988) 662 [INSPIRE].
A. Van Proeyen, Realizations of \( \mathcal{N}=4 \) superconformal algebras on Wolf spaces, Class. Quant. Grav. 6 (1989) 1501 [INSPIRE].
A. Sevrin and G. Theodoridis, \( \mathcal{N}=4 \) superconformal coset theories, Nucl. Phys. B 332 (1990) 380 [INSPIRE].
M. Henneaux, G. Lucena Gómez, J. Park and S.-J. Rey, Super-W ∞ asymptotic symmetry of higher-spin AdS 3 supergravity, JHEP 06 (2012) 037 [arXiv:1203.5152] [INSPIRE].
O. Ohlsson Sax and B. Stefanski Jr., Integrability, spin-chains and the AdS 3 /CFT 2 correspondence, JHEP 08 (2011) 029 [arXiv:1106.2558] [INSPIRE].
M. Gaberdiel, Large \( \mathcal{N}=4 \) holography, in Integrability in gauge and string theory, Utrecht The Netherlands (2013).
S. Elitzur, O. Feinerman, A. Giveon and D. Tsabar, String theory on AdS 3 ×S 3 ×S 3 ×S 1, Phys. Lett. B 449 (1999) 180 [hep-th/9811245] [INSPIRE].
J. de Boer, A. Pasquinucci and K. Skenderis, AdS/CFT dualities involving large 2D \( \mathcal{N}=4 \) superconformal symmetry, Adv. Theor. Math. Phys. 3 (1999) 577 [hep-th/9904073] [INSPIRE].
S. Gukov, E. Martinec, G.W. Moore and A. Strominger, The search for a holographic dual to AdS 3 ×S 3 ×S 3 ×S 1, Adv. Theor. Math. Phys. 9 (2005) 435 [hep-th/0403090] [INSPIRE].
M. Beccaria, C. Candu, M.R. Gaberdiel and M. Groher, \( \mathcal{N}=1 \) extension of minimal model holography, arXiv:1305.1048 [INSPIRE].
P. Bowcock and P. Goddard, Coset constructions and extended conformal algebras, Nucl. Phys. B 305 (1988) 685 [INSPIRE].
D. Altschuler, Quantum equivalence of coset space models, Nucl. Phys. B 313 (1989) 293 [INSPIRE].
P. Goddard, A. Kent and D.I. Olive, Unitary representations of the Virasoro and supervirasoro algebras, Commun. Math. Phys. 103 (1986) 105 [INSPIRE].
M.R. Douglas, G/H conformal field theory, CALT-68-1453, (1987) [INSPIRE].
K. Hornfeck and É. Ragoucy, A coset construction for the super W 3 algebra, Nucl. Phys. B 340 (1990) 225 [INSPIRE].
C.-H. Ahn, K. Schoutens and A. Sevrin, The full structure of the super W 3 algebra, Int. J. Mod. Phys. A 6 (1991) 3467 [INSPIRE].
K. Schoutens and A. Sevrin, Minimal super W N algebras in coset conformal field theories, Phys. Lett. B 258 (1991) 134 [INSPIRE].
R. Gopakumar, A. Hashimoto, I.R. Klebanov, S. Sachdev and K. Schoutens, Strange metals in one spatial dimension, Phys. Rev. D 86 (2012) 066003 [arXiv:1206.4719] [INSPIRE].
C. Ahn, The higher spin currents in the \( \mathcal{N}=1 \) stringy coset minimal model, JHEP 04 (2013) 033 [arXiv:1211.2589] [INSPIRE].
C. Ahn, Higher spin currents with arbitrary N in the \( \mathcal{N}=1 \) stringy coset minimal model, JHEP 07 (2013) 141 [arXiv:1305.5892] [INSPIRE].
M. Isachenkov, I. Kirsch and V. Schomerus, Chiral primaries in strange metals, arXiv:1403.6857 [INSPIRE].
S. Yamaguchi, Y. Ishimoto and K. Sugiyama, AdS 3 /CFT 2 correspondence and space-time \( \mathcal{N}=3 \) superconformal algebra, JHEP 02(1999) 026[hep-th/9902079] [INSPIRE].
R. Argurio, A. Giveon and A. Shomer, Superstring theory on AdS 3 × G/H and boundary \( \mathcal{N}=3 \) superconformal symmetry, JHEP 04(2000) 010[hep-th/0002104][INSPIRE].
R. Argurio, A. Giveon and A. Shomer, The spectrum of \( \mathcal{N}=3 \) string theory on AdS 3 × G/H, JHEP 12 (2000) 025 [hep-th/0011046] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar and A. Saha, Quantum W-symmetry in AdS 3, JHEP 02 (2011) 004 [arXiv:1009.6087] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Rønne, Higher spin AdS 3 supergravity and its dual CFT, JHEP 02 (2012) 109 [arXiv:1111.2139] [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, T. Hartman and S. Raju, Partition functions of holographic minimal models, JHEP 08 (2011) 077 [arXiv:1106.1897] [INSPIRE].
C. Candu and M.R. Gaberdiel, Supersymmetric holography on AdS 3, JHEP 09 (2013) 071 [arXiv:1203.1939] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Rønne, \( \mathcal{N}=1 \) supersymmetric higher spin holography on AdS 3, JHEP 02 (2013) 019 [arXiv:1209.5404] [INSPIRE].
F.A. Bais, P. Bouwknegt, M. Surridge and K. Schoutens, Coset construction for extended Virasoro algebras, Nucl. Phys. B 304 (1988) 371 [INSPIRE].
P. Goddard and A. Schwimmer, Factoring out free fermions and superconformal algebras, Phys. Lett. B 214 (1988) 209 [INSPIRE].
P. Di Francesco, P. Mathieu and D. Senechal, Conformal field theory, Springer, New York U.S.A. (1997) [INSPIRE].
S.G. Naculich and H.J. Schnitzer, Superconformal coset equivalence from level rank duality, Nucl. Phys. B 505 (1997) 727 [hep-th/9705149] [INSPIRE].
K. Miki, The representation theory of the SO(3) invariant superconformal algebra, Int. J. Mod. Phys. A 5 (1990) 1293 [INSPIRE].
W. Lerche, C. Vafa and N.P. Warner, Chiral rings in \( \mathcal{N}=2 \) superconformal theories, Nucl. Phys. B 324 (1989) 427 [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Rønne, Three point functions in higher spin AdS 3 supergravity, JHEP 01 (2013) 171 [arXiv:1211.2237] [INSPIRE].
H. Moradi and K. Zoubos, Three-point functions in \( \mathcal{N}=2 \) higher-spin holography, JHEP 04 (2013) 018 [arXiv:1211.2239] [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].
V.G. Knizhnik, Superconformal algebras in two-dimensions, Theor. Math. Phys. 66 (1986) 68 [Teor. Mat. Fiz. 66 (1986) 102] [INSPIRE].
M.R. Gaberdiel, K. Jin and W. Li, Perturbations of W ∞ CFTs, JHEP 10 (2013) 162 [arXiv:1307.4087] [INSPIRE].
D. Tong, The holographic dual of AdS 3 ×S 3 ×S 3 ×S 1, JHEP 04 (2014) 193 [arXiv:1402.5135] [INSPIRE].
I.G. Macdonald, Symmetric functions and Hall polynomials, Oxford University Press, Oxford U.K. (1998).
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1406.1521
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Creutzig, T., Hikida, Y. & Rønne, P.B. Higher spin AdS3 holography with extended supersymmetry. J. High Energ. Phys. 2014, 163 (2014). https://doi.org/10.1007/JHEP10(2014)163
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2014)163