Operator Approach to Boundary Liouville Theory

Details Operator Approach to Boundary Liouville Theory Operator Approach to Boundary Liouville Theory

2008-01-21

arxiv.org/abs/0801.3206v2

AnnalsPhys.323:2799-2839,2008

Physics

High Energy Physics

High Energy Physics - Theory

45 pages, 5 figures, extented subsection 4.3.2, related minor changes in subsections 3.3 and 4.2

Scientific paper

10.1016/j.aop.2008.02.009

We propose new methods for calculation of the discrete spectrum, the reflection amplitude and the correlation functions of boundary Liouville theory on a strip with Lorentzian signature. They are based on the structure of the vertex operator $V=e^{-\phi}$ in terms of the asymptotic operators. The methods first are tested for the particle dynamics in the Morse potential, where similar structures appear. Application of our methods to boundary Liouville theory reproduces the known results obtained earlier in the bootstrap approach, but there can arise a certain extension when the boundary parameters are near to critical values. Namely, in this case we have found up to four different equidistant series of discrete spectra, and the reflection amplitude is modified respectively.

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