Dualities for 3d Theories with Tensor Matter

TL;DR

The paper develops and tests seven Seiberg-like dualities in 3d ${\\cal N}=2$ Chern-Simons-matter theories with tensor matter across U, O, and Sp gauge groups. Using localization, it computes the $S^3$ partition function and the superconformal index to provide nonperturbative checks, including several cases where a tensor theory without a superpotential is dual to a free theory, generalizing the Jafferis-Yin scenario. It also analyzes nonperturbative truncation of the chiral ring and maps chiral-ring generators between electric and magnetic descriptions, finding broad agreement across many dual pairs. The results illuminate how tensor matter enriches 3d dualities and establish a framework for further explorations of CS levels, moduli spaces, and potential no-superpotential duals. Overall, the work substantiates a rich web of 3d dualities that parallel known 4d constructions while revealing unique 3d phenomena such as monopole-induced truncations.

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.