Integrability of boundary Liouville conformal field theory

Abstract

Liouville conformal field theory (LCFT) is considered on a simply connected domain with boundary, specializing to the case where the Liouville potential is integrated only over the boundary of the domain. We work in the probabilistic framework of boundary LCFT introduced by Huang-Rhodes-Vargas (2015). Building upon the known proof of the bulk one-point function by the first author, exact formulas are rigorously derived for the remaining basic correlation functions of the theory, i.e., the bulk-boundary correlator, the boundary two-point and the boundary three-point functions. These four correlations should be seen as the fundamental building blocks of boundary Liouville theory, playing the analogue role of the DOZZ formula in the case of the Riemann sphere. Our study of boundary LCFT also provides the general framework to understand the integrability of one-dimensional Gaussian multiplicative chaos measures as well as their tail expansions. Finally these results have applications to studying the conformal blocks of CFT and set the stage for the more general case of boundary LCFT with both bulk and boundary Liouville potentials.

arXiv comment70 pages, 2 figures

References in corpus (15)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Two and three-point functions in Liouville theory
• Liouville Field Theory -- A decade after the revolution
• Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U_q(sl(2,R))
• Freezing and extreme value statistics in a Random Energy Model with logarithmically correlated potential
• The Annular Report on Non-Critical String Theory
• Boundary Liouville Field Theory: Boundary Three Point Function
• Statistical Mechanics of Logarithmic REM: Duality, Freezing and Extreme Value Statistics of $1/f$ Noises generated by Gaussian Free Fields
• Bulk-Boundary Propagator in Liouville Theory on a Disc
• Liouville Quantum Gravity on the complex tori
• The Fyodorov-Bouchaud formula and Liouville conformal field theory
• On Barnes Beta Distributions and Applications to the Maximum Distribution of the 2D Gaussian Free Field
• A Review of Conjectured Laws of Total Mass of Bacry-Muzy GMC Measures on the Interval and Circle and Their Applications
• Liouville quantum gravity on the annulus
• Probabilistic conformal blocks for Liouville CFT on the torus

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• Liouville quantum gravity weighted by conformal loop ensemble nesting statistics
• Probabilistic construction of non compactified imaginary Liouville field theory
• A Family of Probability Distributions Consistent with the DOZZ Formula: Towards a Conjecture for the Law of 2D GMC
• The bulk one-arm exponent for the CLE${}_{{\kappa }^{\prime }}$ percolations