Bosonization and Vertex Algebras with Defects

TL;DR

This paper extends bosonization techniques to include point-like defects in 2D space-time, constructing vertex operators and algebras, and applies these to solve models like the massless Thirring model with defects.

Contribution

It introduces a novel framework for bosonization with defects, constructing vertex algebras and representations, and applies it to solve defect-influenced models.

Findings

Constructed vertex operators in the presence of defects

Solved the massless Thirring model with a defect

Built vertex representations of sl(2) Kac-Moody algebra

Abstract

The method of bosonization is extended to the case when a dissipationless point-like defect is present in space-time. Introducing the chiral components of a massless scalar field, interacting with the defect in two dimensions, we construct the associated vertex operators. The main features of the corresponding vertex algebra are established. As an application of this framework we solve the massless Thirring model with defect. We also construct the vertex representation of the sl(2) Kac-Moody algebra, describing the complex interplay between the left and right sectors due to the interaction with the defect. The Sugawara form of the energy-momentum tensor is also explored.