Kramers-Wannier dualities for WZW theories and minimal models

TL;DR

This paper classifies Kramers-Wannier dualities in certain rational conformal field theories, revealing they exist only at small levels and preserving all chiral symmetries, using a topological field theory approach.

Contribution

It provides a classification of dualities in WZW and minimal models that preserve chiral symmetries, highlighting their existence only at small levels.

Findings

Dualities exist only for small levels.

Dualities preserve all chiral symmetries.

Classification achieved via TFT approach.

Abstract

We study Kramers-Wannier dualities for Wess-Zumino-Witten theories and (super-)minimal models in the Cardy case, i.e. the case with bulk partition function given by charge conjugation. Using the TFT approach to full rational conformal field theories, we classify those dualities that preserve all chiral symmetries. Dualities turn out to exist for small levels only.