Liouville conformal field theory on Riemann surface with boundaries

Baojun Wu

Liouville conformal field theory on Riemann surface with boundaries

Probability 2023-01-19 v3 Mathematical Physics math.MP

Authors: Baojun Wu

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.

Keywords

Liouville conformal field theory Riemann surface with boundaries Markov property fusion estimates conformal bootstrap

Cite

@article{arxiv.2203.11721,
  title  = {Liouville conformal field theory on Riemann surface with boundaries},
  author = {Baojun Wu},
  journal= {arXiv preprint arXiv:2203.11721},
  year   = {2023}
}

Comments

21 pages, 2 figures. In this version we have added some fusion-type estimate in Section 6.2. arXiv admin note: text overlap with arXiv:1607.08467 by other authors

Liouville conformal field theory on Riemann surface with boundaries

Abstract

Keywords

Cite

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