Liouville field theory on a pseudosphere
Abstract
Liouville field theory is considered with boundary conditions corresponding to a quantization of the classical Lobachevskiy plane (i.e. euclidean version of $AdS_2$). We solve the bootstrap equations for the outvacuum wave function and find an infinite set of solutions. This solutions are in one to one correspondence with the degenerate representations of the Virasoro algebra. Consistency of these solutions is verified by both boundary and modular bootstrap techniques. Perturbative calculations lead to the conclusion that only the ``basic'' solution corresponding to the identity operator provides a ``natural'' quantization of the Lobachevskiy plane.
 Publication:

arXiv eprints
 Pub Date:
 January 2001
 arXiv:
 arXiv:hepth/0101152
 Bibcode:
 2001hep.th....1152Z
 Keywords:

 High Energy Physics  Theory
 EPrint:
 24 pages, 5 figures