# Exceptional Chern-Simons-Matter Dualities

### Submission summary

 As Contributors: Po-Shen Hsin Arxiv Link: https://arxiv.org/abs/1812.11705v2 (pdf) Date accepted: 2019-10-18 Date submitted: 2019-09-19 02:00 Submitted by: Hsin, Po-Shen Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory High-Energy Physics - Theory Approach: Theoretical

### 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.

### Ontology / Topics

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Published as SciPost Phys. 7, 056 (2019)

### List of changes

- new footnote 8
- replace the word quartic coupling by a suitable potential
- fixed typos mentioned in the report
- update references