Liouville Theory on the Pseudosphere: Bulk-Boundary Structure Constant

TL;DR

This paper computes the bulk-boundary structure constant in Liouville theory on the pseudosphere using two methods, confirming their agreement and advancing understanding of boundary effects in this model.

Contribution

It provides the first explicit calculation of the bulk-boundary structure constant for Dirichlet conditions in Liouville theory on the pseudosphere, validating a proposed relation with Neumann conditions.

Findings

Agreement between the two computational methods

Explicit expression for the bulk-boundary structure constant

Validation of the relation proposed by Hosomichi

Abstract

Liouville field theory on the pseudosphere is considered (Dirichlet conditions). We compute explicitely the bulk-boundary structure constant with two different methods: first we use a suggestion made by Hosomichi in JHEP 0111 (2001) that relates this quantity directly to the bulk-boundary structure constant with Neumann conditions, then we do a direct computation. Agreement is found.