Integrability of Boundary Liouville Conformal Field Theory

Liouville conformal field theory (LCFT) is considered on a simply connected domain with boundary, specializing to the case where potential integrated only over boundary of domain. We work in probabilistic framework LCFT introduced by Huang et al. (Ann Inst H Poincare Probab Statist 54(3):1694–1730, 2018. https://doi.org/10.1214/17-AIHP852 ). Building upon known proof bulk one-point function first author, exact formulas are rigorously derived for remaining basic correlation functions theory, i.e., bulk-boundary correlator, two-point and three-point functions. These four correlations should be seen as fundamental building blocks playing analogous role DOZZ formula Riemann sphere. Our study also provides general understand integrability one-dimensional Gaussian multiplicative chaos measures well their tail expansions. Finally these results have applications studying CFT set stage more both potentials.