Seiberg-like Dualities for 3d N=2 Theories with SU(N) gauge group

TL;DR

This paper derives and verifies Seiberg-like dualities for 3d N=2 SU(N) gauge theories using SL(2,Z) transformations, extending known dualities with new evidence from index computations and chiral ring analysis.

Contribution

It introduces a novel method to obtain SU(N) dualities from U(N) dualities via SL(2,Z) actions and provides detailed dualities including Aharony and Giveon-Kutasov types with supporting evidence.

Findings

Derived new Seiberg-like dualities for SU(N) theories.

Confirmed dualities through superconformal index matching.

Extended dualities to theories with adjoint matter and Chern-Simons terms.

Abstract

We work out Seiberg-like dualities for 3d $\mathcal{N}=2$ theories with SU(N) gauge group. We use the $SL(2,\mathbb{Z})$ action on 3d conformal field theories with U(1) global symmetry. One of generator S of $SL(2,\mathbb{Z})$ acts as gauging of the U(1) global symmetry. Utilizing $S=S^{-1}$ up to charge conjugation, we obtain Seiberg-like dual of SU(N) theories by gauging topological U(1) symmetry of the Seiberg-like dual of U(N) theories with the same matter content. We work out the Aharony dualities for SU(N) gauge theory with $N_f$ fundamental/anti-fundamnetal flavors, with/without one adjoint matter with the superpotential. We also work out the Giveon-Kutasov dualities for SU(N) gauge theory with Chern-Simons term and with $N_f$ fundamental/anti-fundamental flavors. For all the proposed dualities, we give various evidences such as chiral ring matching and the superconformal index computations. We find the perfect matchings.