# Exceptional Chern-Simons-Matter Dualities

## TL;DR

This paper derives new dualities in three-dimensional topological field theories using exceptional affine Kac-Moody algebra embeddings, extending classical level-rank dualities to exceptional gauge groups and proposing related matter dualities.

## Contribution

It introduces novel dualities involving exceptional gauge groups via conformal embeddings, expanding the scope of known Chern-Simons dualities and their applications.

## Key findings

- Derived dualities between exceptional and classical gauge groups.
- Proposed new boson-boson Chern-Simons matter dualities.
- Analyzed phase diagrams of G2 gauge theories with fermions.

## Abstract

We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on classical gauge groups to the setting of exceptional gauge groups. For instance, one duality sequence we discuss is $(E_{N})_{1}\leftrightarrow SU(9-N)_{-1}$. Others such as $SO(3)_{8}\leftrightarrow PSU(3)_{-6},$ are dualities among theories with classical gauge groups that arise due to their embedding into an exceptional chiral algebra. We apply these equivalences between topological field theories to conjecture new boson-boson Chern-Simons matter dualities. We also use them to determine candidate phase diagrams of time-reversal invariant $G_{2}$ gauge theory coupled to either an adjoint fermion, or two fundamental fermions.