From Defects to Boundaries

TL;DR

This paper explores the equivalence between relativistic field theories with defects and boundary theories, applying boundary results to defects, deriving defect unitarity, and calculating groundstate energies.

Contribution

It establishes a formal connection between defect and boundary field theories, enabling the use of boundary techniques for defects and deriving new solutions for defect integrable models.

Findings

Defect crossing unitarity equation derived for integrable theories

Solutions of the defect Yang-Baxter equation obtained for purely transmitting impurities

Groundstate energy on the strip with defects calculated

Abstract

In this paper we describe how relativistic field theories containing defects are equivalent to a class of boundary field theories. As a consequence previously derived results for boundaries can be directly applied to defects, these results include reduction formulas, the Coleman-Thun mechanism and Cutcosky rules. For integrable theories the defect crossing unitarity equation can be derived and defect operator found. For a generic purely transmitting impurity we use the boundary bootstrap method to obtain solutions of the defect Yang-Baxter equation. The groundstate energy on the strip with defects is also calculated.