Abstract
We study black hole solutions in Chern-Simons higher spin supergravity based on the superalgebra sl(3|2). These black hole solutions have a U(1) gauge field and a spin 2 hair in addition to the spin 3 hair. These additional fields correspond to the R-symmetry charges of the supergroup sl(3|2). Using the relation between the bulk field equations and the Ward identities of a CFT with \( \mathcal{N} \) = 2 super-\( {{\mathcal{W}}_3} \) symmetry, we identify the bulk charges and chemical potentials with those of the boundary CFT. From these identifications we see that a suitable set of variables to study this black hole is in terms of the charges present in three decoupled bosonic sub-algebras of the \( \mathcal{N} \) = 2 super-\( {{\mathcal{W}}_3} \) algebra. The entropy and the partition function of these R-charged black holes are then evaluated in terms of the charges of the bulk theory as well as in terms of its chemical potentials. We then compute the partition function in the dual CFT and find exact agreement with the bulk partition function.
Similar content being viewed by others
References
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.R. Gaberdiel and R. Gopakumar, Minimal model holography, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [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. Blencowe, A consistent interacting massless higher spin field theory in D = (2 + 1), Class. Quant. Grav. 6 (1989) 443 [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. 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].
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].
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].
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].
A. Castro, E. Hijano, A. Lepage-Jutier and A. Maloney, Black holes and singularity resolution in higher spin gravity, JHEP 01 (2012) 031 [arXiv:1110.4117] [INSPIRE].
M. Ammon, M. Gutperle, P. Kraus and E. Perlmutter, Spacetime geometry in higher spin gravity, JHEP 10 (2011) 053 [arXiv:1106.4788] [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].
Y. Hikida, Conical defects and N = 2 higher spin holography, arXiv:1212.4124 [INSPIRE].
A. Schwimmer and N. Seiberg, Comments on the N = 2, N = 3, N = 4 superconformal algebras in two-dimensions, Phys. Lett. B 184 (1987) 191 [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].
J.M. Maldacena and L. Maoz, Desingularization by rotation, JHEP 12 (2002) 055 [hep-th/0012025] [INSPIRE].
P. Kraus, Lectures on black holes and the AdS 3 /CF T 2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [INSPIRE].
M. Gutperle and P. Kraus, Higher spin black holes, JHEP 05 (2011) 022 [arXiv:1103.4304] [INSPIRE].
B. Chen, J. Long and Y.-N. Wang, Conical defects, black holes and higher spin (super-)symmetry, JHEP 06 (2013) 025 [arXiv:1303.0109] [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [INSPIRE].
S. Deser and J. Kay, Topologically massive supergravity, Phys. Lett. B 120 (1983) 97 [INSPIRE].
E. Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
A. Achucarro and P. Townsend, A Chern-Simons action for three-dimensional Anti-de Sitter supergravity theories, Phys. Lett. B 180 (1986) 89 [INSPIRE].
J. Izquierdo and P. Townsend, Supersymmetric space-times in (2 + 1) AdS supergravity models, Class. Quant. Grav. 12 (1995) 895 [gr-qc/9501018] [INSPIRE].
X. Bekaert, S. Cnockaert, C. Iazeolla and M. Vasiliev, Nonlinear higher spin theories in various dimensions, hep-th/0503128 [INSPIRE].
L. Romans, The N = 2 super-W (3) algebra, Nucl. Phys. B 369 (1992) 403 [INSPIRE].
L. Frappat, P. Sorba and A. Sciarrino, Dictionary on Lie superalgebras, hep-th/9607161 [INSPIRE].
M. Bañados, R. Canto and S. Theisen, The action for higher spin black holes in three dimensions, JHEP 07 (2012) 147 [arXiv:1204.5105] [INSPIRE].
P. Kraus and T. Ugajin, An entropy formula for higher spin black holes via conical singularities, JHEP 05 (2013) 160 [arXiv:1302.1583] [INSPIRE].
P. Kraus and E. Perlmutter, Partition functions of higher spin black holes and their CFT duals, JHEP 11 (2011) 061 [arXiv:1108.2567] [INSPIRE].
M.R. Gaberdiel, T. Hartman and K. Jin, Higher spin black holes from CFT, JHEP 04 (2012) 103 [arXiv:1203.0015] [INSPIRE].
C. Peng, Dualities from higher-spin supergravity, JHEP 03 (2013) 054 [arXiv:1211.6748] [INSPIRE].
A. Perez, D. Tempo and R. Troncoso, Higher spin gravity in 3D: black holes, global charges and thermodynamics, arXiv:1207.2844 [INSPIRE].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Towards metric-like higher-spin gauge theories in three dimensions, J. Phys. A 46 (2013) 214017 [arXiv:1208.1851] [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].
B. Chen, J. Long and Y.-N. Wang, Phase structure of higher spin black hole, JHEP 03 (2013) 017 [arXiv:1212.6593] [INSPIRE].
A. Perez, D. Tempo and R. Troncoso, Higher spin black hole entropy in three dimensions, arXiv:1301.0847 [INSPIRE].
J. de Boer and J.I. Jottar, Thermodynamics of higher spin black holes in AdS 3, arXiv:1302.0816 [INSPIRE].
H. Moradi and K. Zoubos, Three-point functions in N = 2 higher-spin holography, JHEP 04 (2013) 018 [arXiv:1211.2239] [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].
R. Blumenhagen and A. Wisskirchen, Extension of the N = 2 virasoro algebra by two primary fields of dimension 2 and 3, Phys. Lett. B 343 (1995) 168 [hep-th/9408082] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1303.1946
Rights and permissions
About this article
Cite this article
Datta, S., David, J.R. Black holes in higher spin supergravity. J. High Energ. Phys. 2013, 110 (2013). https://doi.org/10.1007/JHEP07(2013)110
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2013)110