Kramers-Wannier duality from conformal defects

TL;DR

This paper shows how the fusion algebra of conformal defects in 2D conformal field theories encodes internal symmetries and generalizes Kramers-Wannier duality, demonstrated through Ising and three-states Potts models.

Contribution

It introduces a method to extract duality and symmetry information from the fusion algebra of conformal defects in 2D CFTs.

Findings

Fusion algebra encodes internal symmetries.

Generalized Kramers-Wannier duality can be read from defects.

Illustrated with Ising and three-states Potts models.

Abstract

We demonstrate that the fusion algebra of conformal defects of a two-dimensional conformal field theory contains information about the internal symmetries of the theory and allows one to read off generalisations of Kramers-Wannier duality. We illustrate the general mechanism in the examples of the Ising model and the three-states Potts model.