Non-perturbative Tests of Duality Cascades in Three Dimensional Supersymmetric Gauge Theories

TL;DR

This paper uses supersymmetry localization to non-perturbatively test duality cascades in 3d $ ext{N}=3$ supersymmetric gauge theories, confirming conjectured dualities and extending their applicability.

Contribution

It provides the first non-perturbative tests of duality cascades in 3d $ ext{N}=3$ theories via $S^3$ partition functions, validating and broadening the duality framework.

Findings

Confirmed predictions of duality cascades using $S^3$ partition functions.

Extended duality applicability to less supersymmetric and non-brane theories.

Provided a method for generating new dualities in 3d gauge theories.

Abstract

It has been conjectured that duality cascade occurs in the $\mathcal{N}=3$ supersymmetric Yang-Mills Chern-Simons theory with the gauge group $U(N )_k \times U(N+M )_{-k}$ coupled to two bi-fundamental hypermultiplets. The brane picture suggests that this duality cascade can be generalized to a class of 3d $\mathcal{N}=3$ supersymmetric quiver gauge theories coming from so-called Hanany-Witten type brane configurations. In this paper we perform non-perturbative tests of the duality cascades using supersymmetry localization. We focus on $S^3$ partition functions and prove predictions from the duality cascades. We also discuss that our result can be applied to generate new dualities for more general theories which include less supersymmetric theories and theories without brane constructions.