Entanglement and topological interfaces

TL;DR

This paper investigates how topological interfaces in two-dimensional conformal field theories affect entanglement entropy, revealing a subleading contribution interpretable as a relative entropy, with applications to WZW models and toroidal bosonic theories.

Contribution

It introduces a detailed analysis of entanglement entropy modifications due to topological interfaces in 2D CFTs, including reinterpretation of boundaries and explicit examples.

Findings

Leading entanglement entropy remains unchanged by the interface.

Subleading contribution acts as a relative (Kullback-Leibler) entropy.

Reinterpretation of boundaries as topological interfaces provides new insights.

Abstract

In this paper we consider entanglement entropies in two-dimensional conformal field theories in the presence of topological interfaces. Tracing over one side of the interface, the leading term of the entropy remains unchanged. The interface however adds a subleading contribution, which can be interpreted as a relative (Kullback-Leibler) entropy with respect to the situation with no defect inserted. Reinterpreting boundaries as topological interfaces of a chiral half of the full theory, we rederive the left/right entanglement entropy in analogy with the interface case. We discuss WZW models and toroidal bosonic theories as examples.