# Exceptional Chern-Simons-Matter Dualities

### Submission summary

 As Contributors: Po-Shen Hsin Arxiv Link: https://arxiv.org/abs/1812.11705v1 Date submitted: 2019-07-31 Submitted by: Hsin, Po-Shen Submitted to: SciPost Physics Domain(s): Theoretical Subject area: High-Energy Physics - Theory

### 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.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1812.11705v1 on 31 July 2019