Liouville field theory on a pseudosphere

Details Liouville field theory on a pseudosphere Liouville field theory on a pseudosphere

2001-01-23

arxiv.org/abs/hep-th/0101152v1

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 5 figures

Scientific paper

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 out-vacuum 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.

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