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}(EN)1↔SU(9−N)−1. Others such as SO(3)_{8}\leftrightarrow PSU(3)_{-6},SO(3)8↔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}G2 gauge theory coupled to either an adjoint fermion, or two fundamental fermions.
Highlights
In this paper we derive new dualities of three-dimensional Chern-Simons theories, and use them to propose new dualities of Chern-Simons-matter theories
Our results for TQFTs generalize the familiar level-rank dualities of Chern-Simons theories with classical gauge groups which are of the form: SU (N )K ↔ U (K)−N,−N, U (N )K,K±N ↔ U (K)−N,−N∓K, S p(N )K ↔ S p(K)−N, SO(N )K ↔ SO(K)−N, O(N )1K,K−1+L ↔ O(K)1−N,−N+1+L, O(N )0K,K ↔ S pin(K)−N . (1.1)
For (G2)0 coupled to two fundamental fermions, the theory enjoys a U(1) global symmetry and in the quantum phase this symmetry is spontaneously broken leading to a periodic scalar at long distances as in [32, 34, 40,41,42,43]
Summary
In this paper we derive new dualities of three-dimensional Chern-Simons theories, and use them to propose new dualities of Chern-Simons-matter theories. Our results for TQFTs generalize the familiar level-rank dualities of Chern-Simons theories with classical gauge groups which are of the form: SU (N )K ↔ U (K)−N,−N , U (N )K,K±N ↔ U (K)−N,−N∓K ,. Phase diagrams of this sort have been investigated for classical groups in [8, 31,32,33,34]. The transitions to the quantum phases are weakly coupled in dual variables with U(2) gauge groups which are motivated by the TQFT dualities (1.4). For (G2)0 coupled to two fundamental fermions, the theory enjoys a U(1) global symmetry and in the quantum phase this symmetry is spontaneously broken leading to a periodic scalar at long distances as in [32, 34, 40,41,42,43]
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