Dualities for 3d Theories with Tensor Matter

TL;DR

This paper explores dualities in 3d N=2 Chern-Simons matter theories with tensor matter, confirming them through superconformal index and partition function calculations, and extends known dualities to new classes of theories.

Contribution

It introduces new dualities for 3d theories with tensor matter, generalizing 4d dualities and providing explicit tests via superconformal indices and partition functions.

Findings

Superconformal index and partition function match for dual pairs.

Identification of simple dual descriptions for theories with tensor matter.

Extension of the 'Duality Appetizer' to an infinite class of theories.

Abstract

We study dualities for ${\cal N}=2$ 3d Chern-Simons matter theories with gauge groups U/Sp/O, matter in the two-index tensor representations (adjoint/symmetric/antisymmetric) in addition to the fundamental representation, and a superpotential. These dualities are analogous to Kutasov-Schwimmer-Seiberg dualities in 4d. We test them by computing the superconformal index and the partition function on $S^3$ for many dual pairs and find perfect agreement. In some cases we find a simple dual description for theories with tensor matter and no superpotential, thereby generalizing the "Duality Appetizer" of Jafferis and Yin to an infinite class of theories. We also investigate nonperturbative truncation of the chiral ring proposed in the context of 4d dualities.