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Liouville conformal field theory on Riemann surface with boundaries
Baojun Wu · 2022-03-22 · via math.PR updates on arXiv.org

In this note, we give a unified rigorous construction for the Liouville conformal field theory on compact Riemann surface with boundaries for $γ\in (0,2]$ 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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