Defects and Permutation branes in the Liouville field theory

TL;DR

This paper investigates defects and permutation branes in Liouville field theory, deriving reflection amplitudes and identifying two solution types, thereby advancing understanding of boundary conditions in this conformal field theory.

Contribution

It provides explicit equations for permutation branes and defects in Liouville theory, revealing the existence of discrete and continuous solution families.

Findings

Derived reflection amplitudes for defects and permutation branes.

Identified two solution families: discrete and continuous.

Enhanced understanding of boundary conditions in Liouville field theory.

Abstract

The defects and permutation branes for the Liouville field theory are considered. By exploiting cluster condition, equations satisfied by permutation branes and defects reflection amplitudes are obtained. It is shown that two types of solutions exist, discrete and continuous families.