ADE triality via (non-)invertible symmetry gauging

TL;DR

This paper explores a triality among minimal models in conformal field theory, demonstrating how different series are exchanged via gauging invertible and non-invertible symmetries, extending the understanding of their interrelations.

Contribution

It introduces a new non-invertible symmetry gauging that completes the triality among A-, D-, and E-series minimal models.

Findings

A-series and D-series models are exchanged by gauging a $ ext{Z}_2$ symmetry.

A-series and E-series models are exchanged by gauging a non-invertible symmetry.

D-series and E-series models are exchanged by gauging another non-invertible symmetry.

Abstract

It is long known that A-series minimal models and D-series minimal models are exchanged by gauging the invertible $\mathbb{Z}_2$ symmetry. More recently, it has been shown that A-series minimal models and E-series minimal models are exchanged by gauging a non-invertible symmetry. We complete the triality picture by showing that D-series minimal models and E-series minimal models are exchanged by gauging another non-invertible symmetry.