On classical and semiclassical properties of the Liouville theory with defects

TL;DR

This paper investigates the classical and semiclassical aspects of Liouville theory with topological defects, providing solutions to defect equations of motion and analyzing the behavior of defect two-point functions in different limits.

Contribution

It offers a detailed analysis of the defect equations of motion and connects semiclassical limits of the two-point function to classical solutions and path integrals.

Findings

Heavy limit given by exponential of Liouville action with defects

Light limit described by finite-dimensional path integral

Explicit solutions to defect equations of motion

Abstract

The Lagrangian of the Liouville theory with topological defects is analyzed in detail and general solution of the corresponding defect equations of motion is found. We study the heavy and light semiclassical limits of the defect two-point function found before via the bootstrap program. We show that the heavy asymptotic limit is given by the exponential of the Liouville action with defects, evaluated on the solutions with two singular points. We demonstrate that the light asymptotic limit is given by the finite dimensional path integral over solutions of the defect equations of motion with a vanishing energy-momentum tensor.