Skip to main content
Springer Nature Link
Log in

Chiral Liouville gravity

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

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.

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. A. Belavin, A.M. Polyakov and A. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B 241 (1984) 333 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. D. Anninos, W. Li, M. Padi, W. Song and A. Strominger, Warped AdS 3 black holes, JHEP 03 (2009) 130 [arXiv:0807.3040] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. 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].

    Article  ADS  Google Scholar 

  4. M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  5. A. Castro and F. Larsen, Near extremal Kerr entropy from AdS 2 quantum gravity, JHEP 12 (2009) 037 [arXiv:0908.1121] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. 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].

    Article  ADS  Google Scholar 

  7. G. Compère, S. de Buyl, S. Detournay and K. Yoshida, Asymptotic symmetries of Schrödinger spacetimes, JHEP 10 (2009) 032 [arXiv:0908.1402] [INSPIRE].

    Article  ADS  Google Scholar 

  8. M. Guica, K. Skenderis, M. Taylor and B.C. van Rees, Holography for Schrödinger backgrounds, JHEP 02 (2011) 056 [arXiv:1008.1991] [INSPIRE].

    Article  ADS  Google Scholar 

  9. 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].

    Article  ADS  Google Scholar 

  10. S. El-Showk and M. Guica, Kerr/CFT, dipole theories and nonrelativistic CFTs, JHEP 12 (2012) 009 [arXiv:1108.6091] [INSPIRE].

    Article  ADS  Google Scholar 

  11. W. Song and A. Strominger, Warped AdS 3 /Dipole-CFT duality, JHEP 05 (2012) 120 [arXiv:1109.0544] [INSPIRE].

    Article  ADS  Google Scholar 

  12. M. Guica, A Fefferman-Graham-like expansion for null warped AdS 3, arXiv:1111.6978 [INSPIRE].

  13. 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].

    Article  ADS  Google Scholar 

  14. S. Detournay, T. Hartman and D.M. Hofman, Warped conformal field theory, Phys. Rev. D 86 (2012) 124018 [arXiv:1210.0539] [INSPIRE].

    ADS  Google Scholar 

  15. F. David, Conformal field theories coupled to 2D gravity in the conformal gauge, Mod. Phys. Lett. A 3 (1988) 1651 [INSPIRE].

    ADS  Google Scholar 

  16. 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].

    Article  MathSciNet  ADS  Google Scholar 

  17. V. Knizhnik, A.M. Polyakov and A. Zamolodchikov, Fractal structure of 2D quantum gravity, Mod. Phys. Lett. A 3 (1988) 819 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  18. R. Jackiw, Liouville field theory: a two-dimensional model for gravity?, in Quantum Theory Of Gravity, S.m. Christensen ed., (1982) 403.

  19. N. Seiberg, Notes on quantum Liouville theory and quantum gravity, Prog. Theor. Phys. Suppl. 102 (1990) 319 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. J. Teschner, Liouville theory revisited, Class. Quant. Grav. 18 (2001) R153 [hep-th/0104158] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. A.M. Polyakov, Quantum gravity in two-dimensions, Mod. Phys. Lett. A 2 (1987) 893 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  22. G. Compère, W. Song and A. Strominger, New boundary conditions for AdS 3, arXiv:1303.2662 [INSPIRE].

  23. 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 

  24. G. Compère, W. Song and A. Virmani, Microscopics of extremal Kerr from spinning M5 branes, JHEP 10 (2011) 087 [arXiv:1010.0685] [INSPIRE].

    Article  ADS  Google Scholar 

  25. A. Bergman and O.J. Ganor, Dipoles, twists and noncommutative gauge theory, JHEP 10 (2000) 018 [hep-th/0008030] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. 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].

    Article  MathSciNet  ADS  Google Scholar 

  27. 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].

    MathSciNet  ADS  Google Scholar 

  28. 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].

    Article  MathSciNet  ADS  Google Scholar 

  29. E. D’Hoker and R. Jackiw, Liouville field theory, Phys. Rev. D 26 (1982) 3517 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  30. J.-L. Gervais and A. Neveu, New quantum treatment of Liouville field theory, Nucl. Phys. B 224 (1983) 329 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. 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].

    MathSciNet  ADS  Google Scholar 

  32. 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].

    Article  MathSciNet  ADS  Google Scholar 

  33. 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].

  34. J. Teschner, Remarks on Liouville theory with boundary, hep-th/0009138 [INSPIRE].

  35. 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].

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for the Fundamental Laws of Nature, Dept. of Physics, Harvard University, Jefferson 470, 17 Oxford Street, Cambridge, MA, 02138, U.S.A

    Geoffrey Compère, Wei Song & Andrew Strominger

  2. Physique Théorique et Mathématique, Université Libre de Bruxelles, Campus Plaine, CP 231, 1050, Bruxelles, Belgium

    Geoffrey Compère

  3. Radcliffe Institute for Advanced Study, 10 Garden St, Cambridge, MA, 02138, U.S.A

    Andrew Strominger

Authors
  1. Geoffrey Compère
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrew Strominger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Geoffrey Compère.

Additional information

ArXiv ePrint: 1303.2660

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP05(2013)154

Keywords

Search

Navigation