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Liouville conformal field theory on Riemann surface with boundaries (2203.11721v3)
Published 22 Mar 2022 in math.PR, math-ph, and math.MP
Abstract: In this note, we give a unified rigorous construction for the Liouville conformal field theory on compact Riemann surface with boundaries for $\gamma\in (0,2]$ 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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