Exceptional Chern-Simons-Matter dualities

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 ↔ S U ( 9 - N ) - 1 . Others such as S O ( 3 ) 8 ↔ P S U ( 3 ) - 6 , are dualities among theories with classical gauge groups that arise dueto 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.