Abstract
Starting from the Chern-Simons formulation, the two-dimensional dual theory for three-dimensional asymptotically flat Einstein gravity at null infinity is constructed. Solving the constraints together with suitable gauge fixing conditions gives in a first stage a chiral Wess-Zumino-Witten like model based on the Poincaré algebra in three dimensions. The next stage involves a Hamiltonian reduction to a BMS3 invariant Liouville theory. These results are connected to those originally derived in the anti-de Sitter case by rephrasing the latter in a suitable gauge before taking their flat-space limit.
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References
G. ’t Hooft, Dimensional reduction in quantum gravity, gr-qc/9310026 [INSPIRE].
L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [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].
E. Witten, (2+1)-Dimensional Gravity as an Exactly Soluble System, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
E. Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE].
G.W. Moore and N. Seiberg, Taming the conformal zoo, Phys. Lett. B 220 (1989) 422 [INSPIRE].
S. Elitzur, G.W. Moore, A. Schwimmer and N. Seiberg, Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory, Nucl. Phys. B 326 (1989) 108 [INSPIRE].
E. Witten, Nonabelian bosonization in two-dimensions, Commun. Math. Phys. 92 (1984) 455 [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].
M. Bañados, Global charges in Chern-Simons field theory and the (2+1) black hole, Phys. Rev. D 52 (1996) 5816 [hep-th/9405171] [INSPIRE].
S. Carlip, The statistical mechanics of the (2+1)-dimensional black hole, Phys. Rev. D 51 (1995) 632 [gr-qc/9409052] [INSPIRE].
S. Carlip, Quantum gravity in 2+1 dimensions, Cambridge University Press, (1998).
M. Bañados, T. Brotz and M.E. Ortiz, Boundary dynamics and the statistical mechanics of the (2+1)-dimensional black hole, Nucl. Phys. B 545 (1999) 340 [hep-th/9802076] [INSPIRE].
S. Carlip, What we don’t know about BTZ black hole entropy, Class. Quant. Grav. 15 (1998) 3609 [hep-th/9806026] [INSPIRE].
M. Bañados, Three-dimensional quantum geometry and black holes, in Trends in Theoretical Physics II, H. Falomir, R.E. Gamboa Saravi and F.A. Schaposnik eds., volume 484 of American Institute of Physics Conference Series, pg. 147 [hep-th/9901148] [INSPIRE].
R. Floreanini and R. Jackiw, Selfdual Fields as Charge Density Solitons, Phys. Rev. Lett. 59 (1987) 1873 [INSPIRE].
M. Bernstein and J. Sonnenschein, A comment on the quantization of chiral bosons, Phys. Rev. Lett. 60 (1988) 1772 [INSPIRE].
J. Sonnenschein, Chiral bosons, Nucl. Phys. B 309 (1988) 752 [INSPIRE].
P. Salomonson, B. Skagerstam and A. Stern, Canonical quantization of chiral bosons, Phys. Rev. Lett. 62 (1989) 1817 [INSPIRE].
M. Stone, How to make a bosonized Dirac fermion from two bosonized Weyl fermions, ILL-TH-89-23 NSF-ITP-89-97 (1989).
M.-f. Chu, P. Goddard, I. Halliday, D.I. Olive and A. Schwimmer, Quantization of the Wess-Zumino-Witten model on a circle, Phys. Lett. B 266 (1991) 71 [INSPIRE].
L. Caneschi and M. Lysiansky, Chiral quantization of the WZW SU(N) model, Nucl. Phys. B 505 (1997) 701 [hep-th/9605099] [INSPIRE].
P. Forgacs, A. Wipf, J. Balog, L. Feher and L. O’Raifeartaigh, Liouville and Toda Theories as Conformally Reduced WZNW Theories, Phys. Lett. B 227 (1989) 214 [INSPIRE].
A. Alekseev and S.L. Shatashvili, Path Integral Quantization of the Coadjoint Orbits of the Virasoro Group and 2D Gravity, Nucl. Phys. B 323 (1989) 719 [INSPIRE].
M. Bershadsky and H. Ooguri, Hidden SL(n) Symmetry in Conformal Field Theories, Commun. Math. Phys. 126 (1989) 49 [INSPIRE].
L. Cornalba and M.S. Costa, Time dependent orbifolds and string cosmology, Fortsch. Phys. 52 (2004) 145 [hep-th/0310099] [INSPIRE].
G. Barnich, A. Gomberoff and H.A. Gonzalez, The flat limit of three dimensional asymptotically anti-de Sitter spacetimes, Phys. Rev. D 86 (2012) 024020 [arXiv:1204.3288] [INSPIRE].
P. Salomonson, B. Skagerstam and A. Stern, ISO(2,1) chiral models and quantum gravity in (2+1)-dimensions, Nucl. Phys. B 347 (1990) 769 [INSPIRE].
G. Barnich and G. Compere, Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions, Class. Quant. Grav. 24 (2007) F15 Erratum ibid. 24 (2007) 3139 [gr-qc/0610130] [INSPIRE].
G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].
A. Bagchi and R. Fareghbal, BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries, JHEP 10 (2012) 092 [arXiv:1203.5795] [INSPIRE].
A. Strominger, Black hole entropy from near horizon microstates, JHEP 02 (1998) 009 [hep-th/9712251] [INSPIRE].
G. Barnich, Entropy of three-dimensional asymptotically flat cosmological solutions, JHEP 10 (2012) 095 [arXiv:1208.4371] [INSPIRE].
A. Bagchi, S. Detournay, R. Fareghbal and J. Simon, Holography of 3d Flat Cosmological Horizons, arXiv:1208.4372 [INSPIRE].
C.R. Nappi and E. Witten, A WZW model based on a nonsemisimple group, Phys. Rev. Lett. 71 (1993) 3751 [hep-th/9310112] [INSPIRE].
G. Barnich, A. Gomberoff and H.A. Gonzalez, BMS 3 invariant two dimensional field theories as flat limit of Liouville, arXiv:1210.0731 [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].
M. Rooman and P. Spindel, Holonomies, anomalies and the Fefferman-Graham ambiguity in AdS 3 gravity, Nucl. Phys. B 594 (2001) 329 [hep-th/0008147] [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, R. Jackiw and S. Templeton, Three-Dimensional Massive Gauge Theories, Phys. Rev. Lett. 48 (1982) 975 [INSPIRE].
J.M. Figueroa-O’Farrill and S. Stanciu, Nonsemisimple Sugawara constructions, Phys. Lett. B 327 (1994) 40 [hep-th/9402035] [INSPIRE].
J.M. Figueroa-O’Farrill and S. Stanciu, Nonreductive WZW models and their CFTs, Nucl. Phys. B 458 (1996) 137 [hep-th/9506151] [INSPIRE].
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ArXiv ePrint: 1303.1075
Research Director of the Fund for Scientific Research-FNRS Belgium. (Glenn Barnich)
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Barnich, G., González, H.A. Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity. J. High Energ. Phys. 2013, 16 (2013). https://doi.org/10.1007/JHEP05(2013)016
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DOI: https://doi.org/10.1007/JHEP05(2013)016