Abstract
We study conical geometry with the maximal number of fermionic symmetry in the higher spin supergravity described by sl(N + 1|N) ⊕ sl(N + 1|N) Chern-Simons gauge theory. It was proposed that a three dimensional \( \mathcal{N}=2 \) higher spin supergravity is holographically dual to the \( \mathcal{N}=\left( {2,2} \right)\mathbb{C}{{\mathbb{P}}^N} \) Kazama-Suzuki model. Based one the duality, we find a map between conical geometries and primary states in the dual CFT. In particular, we construct geometric solutions corresponding to primary states in the RRsector. The proposal is checked by the comparison of a few charges and by the relation between null vectors and higher spin symmetry.
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References
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. Klebanov and A. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [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].
S. Prokushkin and M.A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3−D 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.R. Gaberdiel and R. Gopakumar, Minimal model holography, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [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].
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. 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].
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. 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].
C. Candu, M.R. Gaberdiel, M. Kelm and C. Vollenweider, Even spin minimal model holography, JHEP 01 (2013) 185 [arXiv:1211.3113] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Rønne, N=1 supersymmetric higher spin holography on AdS 3, JHEP 02 (2013) 019 [arXiv:1209.5404] [INSPIRE].
M. Gutperle and P. Kraus, Higher spin black holes, JHEP 05 (2011) 022 [arXiv:1103.4304] [INSPIRE].
M. Ammon, M. Gutperle, P. Kraus and E. Perlmutter, Black holes in three dimensional higher spin gravity: A review, J. Phys. A 46 (2013) 214001 [arXiv:1208.5182] [INSPIRE].
A. Castro, R. Gopakumar, M. Gutperle and J. Raeymaekers, Conical defects in higher spin theories, JHEP 02 (2012) 096 [arXiv:1111.3381] [INSPIRE].
E. Perlmutter, T. Prochazka and J. Raeymaekers, The semiclassical limit of W N CFTs and Vasiliev theory, JHEP 05 (2013) 007 [arXiv:1210.8452] [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, JHEP 08 (2013) 030 [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 \( \mathcal{N}=2 \) minimal model holography, JHEP 02 (2013) 070 [arXiv:1207.6646] [INSPIRE].
Y. Kazama and H. Suzuki, New \( \mathcal{N}=2 \) superconformal field theories and superstring compactification, Nucl. Phys. B 321 (1989) 232 [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].
K. Ito, Quantum Hamiltonian reduction and \( \mathcal{N}=2 \) coset models, Phys. Lett. B 259 (1991) 73 [INSPIRE].
C. Candu and M.R. Gaberdiel, Supersymmetric holography on AdS 3, arXiv:1203.1939 [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Ronne, 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].
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, JHEP 01 (2013) 146 [arXiv:1208.3921] [INSPIRE].
C. Peng, Dualities from higher-spin supergravity, JHEP 03 (2013) 054 [arXiv:1211.6748] [INSPIRE].
L. Frappat, P. Sorba and A. Sciarrino, Dictionary on Lie superalgebras, hep-th/9607161 [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].
D. Gepner, Field identification in coset conformal field theories, Phys. Lett. B 222 (1989) 207 [INSPIRE].
P. Di Francesco, P. Mathieu and D. Senechal, Conformal field theory, Springer, U.S.A. (1997).
K. Ito, \( \mathcal{N}=2 \) superconformal CP n model, Nucl. Phys. B 370 (1992) 123 [INSPIRE].
A. Bilal, Introduction to W algebras, Proceedings of String theory and quantum gravity ’91, Trieste, Italy 1991, pg. 245-280, and CERN Geneva - TH. 6083 (91/04,rec.Jul.).
P. Bouwknegt and K. Schoutens, W symmetry in conformal field theory, Phys. Rept. 223 (1993) 183 [hep-th/9210010] [INSPIRE].
J. Evans and T.J. Hollowood, Supersymmetric Toda field theories, Nucl. Phys. B 352 (1991) 723 [Erratum ibid. B 382 (1992) 662] [INSPIRE].
S. Komata, K. Mohri and H. Nohara, Classical and quantum extended superconformal algebra, Nucl. Phys. B 359 (1991) 168 [INSPIRE].
H. Ozer, On the superfield realization of superCasimir WA n algebras, Int. J. Mod. Phys. A 17 (2002) 317 [hep-th/0102203] [INSPIRE].
M. Henneaux, L. Maoz and A. Schwimmer, Asymptotic dynamics and asymptotic symmetries of three-dimensional extended AdS supergravity, Annals Phys. 282 (2000) 31 [hep-th/9910013] [INSPIRE].
A. Schwimmer and N. Seiberg, Comments on the \( \mathcal{N}=2,\mathcal{N}=3,\mathcal{N}=4 \) superconformal algebras in two-dimensions, Phys. Lett. B 184 (1987) 191 [INSPIRE].
W. Lerche, C. Vafa and N.P. Warner, Chiral rings in \( \mathcal{N}=2 \) superconformal theories, Nucl. Phys. B 324 (1989) 427 [INSPIRE].
D. Gepner, Scalar field theory and string compactification, Nucl. Phys. B 322 (1989) 65 [INSPIRE].
M. Niedermaier, Irrational free field resolutions for W (sl(n)) and extended Sugawara construction, Commun. Math. Phys. 148 (1992) 249 [INSPIRE].
E. Fradkin and V.Y. Linetsky, Supersymmetric Racah basis, family of infinite dimensional superalgebras, SU(∞ + 1|∞) and related 2-D models, Mod. Phys. Lett. A 6 (1991) 617 [INSPIRE].
M. Kato and S. Matsuda, Null field construction in conformal and superconformal algebras, Adv. Stud. Pure Math. 16 (1988) 205. [INSPIRE].
C. Candu and C. Vollenweider, The N = 1 algebra W ∞[μ] and its truncations, arXiv:1305.0013 [INSPIRE].
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ArXiv ePrint: 1212.4124
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Hikida, Y. Conical defects and \( \mathcal{N}=2 \) higher spin holography. J. High Energ. Phys. 2013, 127 (2013). https://doi.org/10.1007/JHEP08(2013)127
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DOI: https://doi.org/10.1007/JHEP08(2013)127