Translation invariant defects as an extension of topological symmetries

TL;DR

This paper extends the concept of topological defects in 2d quantum field theories to translation invariant defects, forming a larger monoidal category and providing a perturbative description, with examples from Ising and Lee-Yang CFTs.

Contribution

It introduces translation invariant defects as an extension of topological defects, enriching the categorical framework and offering a perturbative approach in perturbed conformal field theories.

Findings

Translation invariant defects form a monoidal category containing topological defects.

Some translation invariant defects persist even when topological defects do not after deformation.

Perturbative description via chiral 3D topological field theory is provided.

Abstract

The modern way to understand symmetries of a quantum field theory is via its topological defects in various dimensions. In this contribution to the proceedings we focus on line defects in 2d QFT and we point out that topological defects naturally embed into a larger class, namely translation invariant defects. The latter still allow for non-singular fusion and one obtains a monoidal category of translation invariant defects which contains that of topological defects as a full subcategory. We give a simple perturbative description of translation invariant defects in a perturbed conformal field theory via chiral three-dimensional topological field theory. We show in the example of the Ising CFT and the Lee-Yang CFT that even if no topological defects survive the deformation, some translation invariant defects still do.