Skip to main content
Springer Nature Link
Log in

Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. ’t Hooft, Dimensional reduction in quantum gravity, gr-qc/9310026 [INSPIRE].

  2. L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. 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].

  4. A. Achucarro and P. Townsend, A Chern-Simons Action for three-dimensional anti-de Sitter supergravity theories, Phys. Lett. B 180 (1986) 89 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  5. E. Witten, (2+1)-Dimensional Gravity as an Exactly Soluble System, Nucl. Phys. B 311 (1988) 46 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. E. Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. G.W. Moore and N. Seiberg, Taming the conformal zoo, Phys. Lett. B 220 (1989) 422 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  8. 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].

    Article  MathSciNet  ADS  Google Scholar 

  9. E. Witten, Nonabelian bosonization in two-dimensions, Commun. Math. Phys. 92 (1984) 455 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. 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].

    Article  ADS  MATH  Google Scholar 

  11. 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].

    Google Scholar 

  12. S. Carlip, The statistical mechanics of the (2+1)-dimensional black hole, Phys. Rev. D 51 (1995) 632 [gr-qc/9409052] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  13. S. Carlip, Quantum gravity in 2+1 dimensions, Cambridge University Press, (1998).

  14. 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].

    Article  ADS  Google Scholar 

  15. S. Carlip, What we don’t know about BTZ black hole entropy, Class. Quant. Grav. 15 (1998) 3609 [hep-th/9806026] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. 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].

  17. R. Floreanini and R. Jackiw, Selfdual Fields as Charge Density Solitons, Phys. Rev. Lett. 59 (1987) 1873 [INSPIRE].

    Article  ADS  Google Scholar 

  18. M. Bernstein and J. Sonnenschein, A comment on the quantization of chiral bosons, Phys. Rev. Lett. 60 (1988) 1772 [INSPIRE].

    Article  ADS  Google Scholar 

  19. J. Sonnenschein, Chiral bosons, Nucl. Phys. B 309 (1988) 752 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. P. Salomonson, B. Skagerstam and A. Stern, Canonical quantization of chiral bosons, Phys. Rev. Lett. 62 (1989) 1817 [INSPIRE].

    Article  ADS  Google Scholar 

  21. M. Stone, How to make a bosonized Dirac fermion from two bosonized Weyl fermions, ILL-TH-89-23 NSF-ITP-89-97 (1989).

  22. 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].

    MathSciNet  ADS  Google Scholar 

  23. L. Caneschi and M. Lysiansky, Chiral quantization of the WZW SU(N) model, Nucl. Phys. B 505 (1997) 701 [hep-th/9605099] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. 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].

    MathSciNet  ADS  Google Scholar 

  25. 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].

    Article  MathSciNet  ADS  Google Scholar 

  26. M. Bershadsky and H. Ooguri, Hidden SL(n) Symmetry in Conformal Field Theories, Commun. Math. Phys. 126 (1989) 49 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. L. Cornalba and M.S. Costa, Time dependent orbifolds and string cosmology, Fortsch. Phys. 52 (2004) 145 [hep-th/0310099] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. 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].

    ADS  Google Scholar 

  29. 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].

    Article  MathSciNet  ADS  Google Scholar 

  30. 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].

  31. G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. A. Bagchi and R. Fareghbal, BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries, JHEP 10 (2012) 092 [arXiv:1203.5795] [INSPIRE].

    Article  ADS  Google Scholar 

  33. A. Strominger, Black hole entropy from near horizon microstates, JHEP 02 (1998) 009 [hep-th/9712251] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. G. Barnich, Entropy of three-dimensional asymptotically flat cosmological solutions, JHEP 10 (2012) 095 [arXiv:1208.4371] [INSPIRE].

    Article  ADS  Google Scholar 

  35. A. Bagchi, S. Detournay, R. Fareghbal and J. Simon, Holography of 3d Flat Cosmological Horizons, arXiv:1208.4372 [INSPIRE].

  36. C.R. Nappi and E. Witten, A WZW model based on a nonsemisimple group, Phys. Rev. Lett. 71 (1993) 3751 [hep-th/9310112] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. G. Barnich, A. Gomberoff and H.A. Gonzalez, BMS 3 invariant two dimensional field theories as flat limit of Liouville, arXiv:1210.0731 [INSPIRE].

  38. 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].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. 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].

    Article  MathSciNet  ADS  Google Scholar 

  40. S. Deser, R. Jackiw and S. Templeton, Topologically Massive Gauge Theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [INSPIRE].

  41. S. Deser, R. Jackiw and S. Templeton, Three-Dimensional Massive Gauge Theories, Phys. Rev. Lett. 48 (1982) 975 [INSPIRE].

    Article  ADS  Google Scholar 

  42. J.M. Figueroa-O’Farrill and S. Stanciu, Nonsemisimple Sugawara constructions, Phys. Lett. B 327 (1994) 40 [hep-th/9402035] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  43. J.M. Figueroa-O’Farrill and S. Stanciu, Nonreductive WZW models and their CFTs, Nucl. Phys. B 458 (1996) 137 [hep-th/9506151] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050, Bruxelles, Belgium

    Glenn Barnich

  2. Departamento de Física, P. Universidad Católica de Chile, Casilla 306, Santiago 22, Chile

    Hernán A. González

Authors
  1. Glenn Barnich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hernán A. González
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Glenn Barnich.

Additional information

ArXiv ePrint: 1303.1075

Research Director of the Fund for Scientific Research-FNRS Belgium. (Glenn Barnich)

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP05(2013)016

Keywords

Search

Navigation