3d $\mathcal{N}=2$ dualities for $SU(N_c)\times U(1)$ Chern-Simons gauge theories

TL;DR

This paper systematically derives and verifies 3d $ ext{N}=2$ dualities for $U(N_c)$ gauge theories with different Chern-Simons levels, using gauging procedures and exact partition function identities, expanding the understanding of dualities in these models.

Contribution

It introduces new dualities for 3d $ ext{N}=2$ $U(N_c)$ gauge theories with varied CS levels, derived through gauging and contact term methods, and confirms them via exact partition function identities.

Findings

Derived dualities for various 3d $ ext{N}=2$ $U(N_c)$ theories with different CS levels.

Confirmed dualities through exact three-sphere partition function identities.

Extended duality web to models with adjoint matter, chiral matter, and real mass flows.

Abstract

We systematically study 3d $\mathcal{N}=2$ dualities for $U(N_c)$ gauge theories with different CS levels for the abelian and the non-abelian factors. We derive such dualities by a gauging/ungauging procedure on other known dualities and by adding an opportune CS contact term for the baryonic symmetry. This allows us to follow the various steps on the three sphere partition function, obtaining exact identities among the new dual phases proposed here. We apply the procedure to various cases, namely SQCD without and with adjoint, chiral dualities and some sporadic cases arising from the real mass flow of models with an $E_7 \times U(1)$ enhancement of the global symmetry.