N=2 Dualities and Z Extremization in Three Dimensions

TL;DR

This paper employs localization techniques to verify dualities in three-dimensional N=2 supersymmetric gauge theories, confirming the equivalence of partition functions and supporting the validity of proposed dualities involving unitary, symplectic, and Chern-Simons gauge groups.

Contribution

It demonstrates the use of matrix model computations to confirm dualities in 3D N=2 theories, including cases with non-trivial anomalous dimensions and Chern-Simons terms.

Findings

Partition functions match on both sides of dualities

Strong evidence supports the proposed dualities

Insights into IR conformal dimensions using localization

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.