Boundary Liouville Field Theory: Boundary Three Point Function

TL;DR

This paper derives an explicit formula for the boundary three-point function in Liouville field theory with conformally invariant boundary conditions, advancing understanding of boundary conformal blocks and their monodromy.

Contribution

It provides the first explicit expression for boundary three-point functions in Liouville theory, linking fusion coefficients to boundary correlators.

Findings

Explicit boundary three-point function formula derived

Connection established between fusion coefficients and boundary correlators

Enhances understanding of boundary conformal blocks in Liouville theory

Abstract

Liouville field theory is considered on domains with conformally invariant boundary conditions. We present an explicit expression for the three point function of boundary fields in terms of the fusion coefficients which determine the monodromy properties of the conformal blocks.