Liouville conformal field theory on Riemann surface with boundaries
Abstract
In this note, we give a unified rigorous construction for the Liouville conformal field theory on compact Riemann surface with boundaries for γ∈ (0,2] and prove a certain type of Markov property. We also prove some fusion-type estimates in the Boundary LCFT. This note will serve as a reference for a program leading to the conformal bootstrap for the Riemann surface with boundaries and several related projects.
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