Kramers-Wannier dualities via symmetries

TL;DR

This paper reveals that Kramers-Wannier dualities in lattice models can be derived from symmetry transformations in the associated conformal field theories, highlighting that self-dual models possess an auto-orbifold property.

Contribution

It establishes a direct link between dualities in lattice models and symmetry transformations in conformal field theories, identifying conditions for self-duality.

Findings

Dualities are derived from boundary state symmetries.

Self-duality models have an auto-orbifold property.

Explicit connection between lattice dualities and CFT symmetries.

Abstract

Kramers-Wannier dualities in lattice models are intimately connected with symmetries. We show that they can be found directly and explicitly from the symmetry transformations of the boundary states in the underlying conformal field theory. Intriguingly the only models with a self-duality transformation turn out to be those with an auto-orbifold property.