A note on conical solutions in 3D Vasiliev theory

[en] We construct a class of smooth solutions in three-dimensional Vasiliev higher spin theories based on the gauge algebra hs[lambda]. These solutions naturally generalize the previously constructed conical defect solutions in higher spin theories with sl(N) gauge algebra, to which they reduce when lambda is taken to be equal to N. We provide evidence for their identification with specific primary states of the W_infty [lambda] algebra in a particular classical limit. In terms of the Gaberdiel-Gopakumar-'t Hooft limit of the W_N minimal models, this limit corresponds to a regime where the 't Hooft coupling becomes large.

Disciplines :

Physics

Author, co-author :

Campoleoni, Andrea

Prochazka, Tomas

Raeymaekers, Joris

Language :

English

Title :

A note on conical solutions in 3D Vasiliev theory

Publication date :

10 May 2013

Journal title :

Journal of High Energy Physics

ISSN :

1126-6708

eISSN :

1029-8479

Publisher :

Springer, Heidelberg, Germany

Volume :

1305

Issue :

052

Pages :

1-21

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi UMONS :

since 04 December 2016

Statistics

Number of views

11 (0 by UMONS)

Number of downloads

0 (0 by UMONS)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

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 ].
S. Prokushkin and M.A. Vasiliev, 3D higher spin gauge theories with matter, hep-th/9812242 [ INSPIRE ].
M.R. Gaberdiel and R. Gopakumar, An AdS3 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 ].
T. Creutzig, Y. Hikida and P.B. Ronne, Higher spin AdS3 supergravity and its dual CFT, JHEP 02 (2012) 109 [ arXiv:1111.2139 ] [ INSPIRE ].
C. Candu and M.R. Gaberdiel, Supersymmetric holography on AdS 3, arXiv:1203.1939 [ 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 ].
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 ].
B.L. Feigin, The Lie algebras gl λ and cohomologies of Lie algebras of differential operators, Russ. Math. Surv. 43 (1988) 169.
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 ].
M.P. Blencowe, A consistent interacting massless higher spin field theory in D = (2 + 1), Class. Quant. Grav. 6 (1989) 443 [ INSPIRE ].
E. Bergshoeff, M.P. Blencowe and K.S. Stelle, Area preserving diffeomorphisms and higher spin algebra, Commun. Math. Phys. 128 (1990) 213 [ INSPIRE ].
A. Castro, R. Gopakumar, M. Gutperle and J. Raeymaekers, Conical defects in higher spin theories, JHEP 02 (2012) 096 [ arXiv:1111.3381 ] [ INSPIRE ].
H.S. 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 ].
Y. Hikida, Conical defects and N = 2 higher spin holography, arXiv:1212.4124 [ INSPIRE ].
B. Chen, J. Long and Y.-N. Wang, Conical defects, black holes and higher spin (super-)symmetry, arXiv:1303.0109 [ INSPIRE ].
E. Witten, Quantization of Chern-Simons gauge theory with complex gauge group, Commun. Math. Phys. 137 (1991) 29 [ INSPIRE ].
C. Pope, L. Romans and X. Shen, W∞ and the Racah-Wigner algebra, Nucl. Phys. B 339 (1990) 191 [ 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 ].
C. Iazeolla and P. Sundell, Biaxially symmetric solutions to 4D higher-spin gravity, arXiv:1208.4077 [INSPIRE].
M.A. Vasiliev, Higher spin algebras and quantization on the sphere and hyperboloid, Int. J. Mod. Phys. A 6 (1991) 1115 [ INSPIRE ].
B. Khesin and F. Malikov, Universal Drinfeld-Sokolov reduction and matrices of complex size, Commun. Math. Phys. 175 (1996) 113 [ hep-th/9405116 ] [ INSPIRE ].
V. Drinfeld and V. Sokolov, Lie algebras and equations of Korteweg-de Vries type, J. Sov. Math. 30 (1984) 1975 [ INSPIRE ].
P. Kraus and E. Perlmutter, Probing higher spin black holes, JHEP 02 (2013) 096 [ arXiv:1209.4937 ] [ INSPIRE ].
M.R. Gaberdiel and R. Gopakumar, Triality in minimal model holography, JHEP 07 (2012) 127 [ arXiv:1205.2472 ] [ INSPIRE ].
P. Bouwknegt and K. Schoutens, W symmetry in conformal field theory, Phys. Rept. 223 (1993) 183 [ hep-th/9210010 ] [ INSPIRE ].
E. Perlmutter, T. Prochazka and J. Raeymaekers, The semiclassical limit of WN CFTs and Vasiliev theory, arXiv:1210.8452 [ INSPIRE ].
E. Hijano, P. Kraus and E. Perlmutter, Matching four-point functions in higher spin AdS3 /CFT2, arXiv:1302.6113 [ INSPIRE ].
A. Jevicki and J. Yoon, Field theory of primaries in WN minimal models, arXiv:1302.3851 [ 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, A semi-local holographic minimal model, arXiv:1302.4420 [ INSPIRE ].
C.-M. Chang and X. Yin, Correlators in WN minimal model revisited, JHEP 10 (2012) 050 [ arXiv:1112.5459 ] [ INSPIRE ].
J.R. David, M. Ferlaino and S.P. Kumar, Thermodynamics of higher spin black holes in 3D, JHEP 11 (2012) 135 [ arXiv:1210.0284 ] [ INSPIRE ].
S.H. Shenker and X. Yin, Vector models in the singlet sector at finite temperature, arXiv:1109.3519 [ INSPIRE ].
S. Banerjee et al., Smoothed transitions in higher spin AdS gravity, arXiv:1209.5396 [ INSPIRE ].
B. Chen, J. Long and Y.-N. Wang, Phase structure of higher spin black hole, JHEP 03 (2013) 017 [ arXiv:1212.6593 ] [ INSPIRE ].
J. de Boer and J.I. Jottar, Thermodynamics of higher spin black holes in AdS3, arXiv:1302.0816 [ INSPIRE ].
E. Fradkin and V.Y. Linetsky, Infinite dimensional generalizations of finite dimensional symmetries, J. Math. Phys. 32 (1991) 1218 [ INSPIRE ].