Abstract
Classical two-dimensional Liouville gravity is often considered in conformal gauge which has a residual left and right Virasoro symmetry algebra. We consider an alternate, chiral, gauge which has a residual right Virasoro Kac-Moody algebra, and no left Virasoro algebra. The Kac-Moody zero mode is the left-moving energy. Dirac brackets of the constrained Hamiltonian theory are derived, and the residual symmetries are shown to be generated by integrals of the conserved chiral currents. The central charge and Kac-Moody level are computed. The possible existence of a corresponding quantum theory is discussed.
Similar content being viewed by others
References
A. Belavin, A.M. Polyakov and A. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B 241 (1984) 333 [INSPIRE].
D. Anninos, W. Li, M. Padi, W. Song and A. Strominger, Warped AdS 3 black holes, JHEP 03 (2009) 130 [arXiv:0807.3040] [INSPIRE].
G. Compère and S. Detournay, Semi-classical central charge in topologically massive gravity, Class. Quant. Grav. 26 (2009) 012001 [Erratum ibid. 26 (2009) 139801] [arXiv:0808.1911] [INSPIRE].
M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].
A. Castro and F. Larsen, Near extremal Kerr entropy from AdS 2 quantum gravity, JHEP 12 (2009) 037 [arXiv:0908.1121] [INSPIRE].
G. Compère and S. Detournay, Boundary conditions for spacelike and timelike warped AdS 3 spaces in topologically massive gravity, JHEP 08 (2009) 092 [arXiv:0906.1243] [INSPIRE].
G. Compère, S. de Buyl, S. Detournay and K. Yoshida, Asymptotic symmetries of Schrödinger spacetimes, JHEP 10 (2009) 032 [arXiv:0908.1402] [INSPIRE].
M. Guica, K. Skenderis, M. Taylor and B.C. van Rees, Holography for Schrödinger backgrounds, JHEP 02 (2011) 056 [arXiv:1008.1991] [INSPIRE].
D.M. Hofman and A. Strominger, Chiral scale and conformal invariance in 2D quantum field theory, Phys. Rev. Lett. 107 (2011) 161601 [arXiv:1107.2917] [INSPIRE].
S. El-Showk and M. Guica, Kerr/CFT, dipole theories and nonrelativistic CFTs, JHEP 12 (2012) 009 [arXiv:1108.6091] [INSPIRE].
W. Song and A. Strominger, Warped AdS 3 /Dipole-CFT duality, JHEP 05 (2012) 120 [arXiv:1109.0544] [INSPIRE].
M. Guica, A Fefferman-Graham-like expansion for null warped AdS 3, arXiv:1111.6978 [INSPIRE].
T. Azeyanagi, D.M. Hofman, W. Song and A. Strominger, The spectrum of strings on warped AdS 3× S 3, JHEP 04 (2013) 078 [arXiv:1207.5050] [INSPIRE].
S. Detournay, T. Hartman and D.M. Hofman, Warped conformal field theory, Phys. Rev. D 86 (2012) 124018 [arXiv:1210.0539] [INSPIRE].
F. David, Conformal field theories coupled to 2D gravity in the conformal gauge, Mod. Phys. Lett. A 3 (1988) 1651 [INSPIRE].
J. Distler and H. Kawai, Conformal field theory and 2D quantum gravity or who’s afraid of Joseph Liouville?, Nucl. Phys. B 321 (1989) 509 [INSPIRE].
V. Knizhnik, A.M. Polyakov and A. Zamolodchikov, Fractal structure of 2D quantum gravity, Mod. Phys. Lett. A 3 (1988) 819 [INSPIRE].
R. Jackiw, Liouville field theory: a two-dimensional model for gravity?, in Quantum Theory Of Gravity, S.m. Christensen ed., (1982) 403.
N. Seiberg, Notes on quantum Liouville theory and quantum gravity, Prog. Theor. Phys. Suppl. 102 (1990) 319 [INSPIRE].
J. Teschner, Liouville theory revisited, Class. Quant. Grav. 18 (2001) R153 [hep-th/0104158] [INSPIRE].
A.M. Polyakov, Quantum gravity in two-dimensions, Mod. Phys. Lett. A 2 (1987) 893 [INSPIRE].
G. Compère, W. Song and A. Strominger, New boundary conditions for AdS 3, arXiv:1303.2662 [INSPIRE].
O. Coussaert, M. Henneaux and P. van Driel, The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant, Class. Quant. Grav. 12 (1995) 2961 [gr-qc/9506019] [INSPIRE].
G. Compère, W. Song and A. Virmani, Microscopics of extremal Kerr from spinning M5 branes, JHEP 10 (2011) 087 [arXiv:1010.0685] [INSPIRE].
A. Bergman and O.J. Ganor, Dipoles, twists and noncommutative gauge theory, JHEP 10 (2000) 018 [hep-th/0008030] [INSPIRE].
K. Dasgupta, O.J. Ganor and G. Rajesh, Vector deformations of N = 4 super Yang-Mills theory, pinned branes and arched strings, JHEP 04 (2001) 034 [hep-th/0010072] [INSPIRE].
A. Bergman, K. Dasgupta, O.J. Ganor, J.L. Karczmarek and G. Rajesh, Nonlocal field theories and their gravity duals, Phys. Rev. D 65 (2002) 066005 [hep-th/0103090] [INSPIRE].
T.L. Curtright and C.B. Thorn, Conformally invariant quantization of the Liouville theory, Phys. Rev. Lett. 48 (1982) 1309 [Erratum ibid. 48 (1982) 1768] [INSPIRE].
E. D’Hoker and R. Jackiw, Liouville field theory, Phys. Rev. D 26 (1982) 3517 [INSPIRE].
J.-L. Gervais and A. Neveu, New quantum treatment of Liouville field theory, Nucl. Phys. B 224 (1983) 329 [INSPIRE].
E. D’Hoker, D.Z. Freedman and R. Jackiw, SO(2,1) invariant quantization of the Liouville theory, Phys. Rev. D 28 (1983) 2583 [INSPIRE].
A.B. Zamolodchikov and A.B. Zamolodchikov, Structure constants and conformal bootstrap in Liouville field theory, Nucl. Phys. B 477 (1996) 577 [hep-th/9506136] [INSPIRE].
V. Fateev, A.B. Zamolodchikov and A.B. Zamolodchikov, Boundary Liouville field theory. 1. Boundary state and boundary two point function, hep-th/0001012 [INSPIRE].
J. Teschner, Remarks on Liouville theory with boundary, hep-th/0009138 [INSPIRE].
L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville correlation functions from four-dimensional gauge theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1303.2660
Rights and permissions
About this article
Cite this article
Compère, G., Song, W. & Strominger, A. Chiral Liouville gravity. J. High Energ. Phys. 2013, 154 (2013). https://doi.org/10.1007/JHEP05(2013)154
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2013)154