Aspects of diffeomorphism and conformal invariance in classical Liouville theory

¹  S.N. Bose National Centre for Basic Sciences - JD Block, Sector III, Salt Lake, Kolkata-700098, India
²  Department of Physics, University of Helsinki and Helsinki Institute of Physics - P.O.Box 64, FIN-00014 Helsinki, Finland, EU
³  Department of Physics and Astrophysics, West Bengal State University - Barasat, India
⁴  Harish-Chandra Research Institute - Chhatnag Road, Jhusi, Allahabad 211019, India

Corresponding authors: rabin@bose.res.in sunandan.gangopadhyay@gmail.com sunandan@bose.res.in shailesh@bose.res.in

Received: 8 September 2009
Accepted: 10 December 2009

Abstract

The interplay between the diffeomorphism and conformal symmetries (a feature common in quantum field theories) is shown to be exhibited for the case of black holes in two-dimensional classical Liouville theory. We show that although the theory is conformally invariant in the near-horizon limit, there is a breaking of the diffeomorphism symmetry at the classical level. On the other hand, in the region away from the horizon, the conformal symmetry of the theory gets broken with the diffeomorphism symmetry remaining intact.