N=2 Dualities and Z Extremization in Three Dimensions

TL;DR

The paper develops and tests N=2 dualities in three dimensions using localization to a matrix-model partition function. By mapping chiral and gauge contributions, and incorporating real mass and FI deformations, it provides strong evidence for Aharony-Seiberg dualities (unitary and symplectic) and Giveon-Kutasov dualities, including CS terms, via exact partition-function equalities tied to hyperbolic gamma function identities. It also discusses how the IR R-symmetry can be constrained by extremizing the absolute partition function, with illustrative examples showing cases where the IR theory becomes free or where analytic continuation is required. Overall, the work clarifies the role of holomorphy, mass deformations, and CS terms in establishing and understanding 3D N=2 dualities and their IR structure.

Abstract

We use localization techniques to study duality in N = 2 supersymmetric gauge theories in three dimensions. Specifically, we consider a duality due to Aharony involving unitary and symplectic gauge groups, which is similar to Seiberg duality in four dimensions, as well as related dualities involving Chern-Simons terms. These theories have the possibility of non-trivial anomalous dimensions for the chiral multiplets and were previously difficult to examine. We use a matrix model to compute the partition functions on both sides of the duality, deformed by real mass and FI terms, and find that they agree. The results provide strong evidence for the validity of the proposed dualities. We also comment on a recent proposal for recovering the exact IR conformal dimensions in such theories using localization.