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Liouville field theory on a pseudosphere

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arxiv hep-th/0101152 v1 pith:HM33W2AO submitted 2001-01-23 hep-th

classification hep-th
keywords solutionsbootstrapboundarycorrespondingfieldliouvillelobachevskiyplane
verification ladder T0 review T1 audit T2 compute T3 formal
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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 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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