Bosonization and Vertex Algebras with Defects

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 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{sl}(2)$$\end{document} affine Lie algebra, describing the complex interplay between the left and right sectors, which is a direct consequence of the interaction with the defect. The Sugawara form of the energy-momentum tensor is also explored.