Nonperturbative Tests of Three-Dimensional Dualities

TL;DR

The paper develops a nonperturbative framework for testing three-dimensional dualities by computing exact $S^3$ partition functions via localization and a derived matrix model. It verifies mirror symmetry for abelian and nonabelian quivers by showing that FI and real-mass deformations are exchanged under duality, with a key use of Cauchy determinant identities to manifest the symmetry in the nonabelian case. It furthermore tests the ABJM/$\mathcal{N}=8$ SYM duality at unit Chern-Simons level by demonstrating a precise partition-function equality under a parameter mapping, thus providing strong nonperturbative evidence for these dualities and their holographic implications. The results consolidate the role of exact partition functions as a robust, nonperturbative probe of IR dualities in 3D SCFTs and illuminate the structure of parameter maps between dual theories.

Abstract

We test several conjectural dualities between strongly coupled superconformal field theories in three dimensions by computing their exact partition functions on a three-sphere as a function of Fayet-Iliopoulos and mass parameters. The calculation is carried out using localization of the path integral and the matrix model previously derived for superconformal N = 2 gauge theories. We verify that the partition functions of quiver theories related by mirror symmetry agree provided the mass parameters and the Fayet-Iliopoulos parameters are exchanged, as predicted. We carry out a similar calculation for the mirror of N = 8 super-Yang-Mills theory and show that its partition function agrees with that of the ABJM theory at unit Chern-Simons level. This provides a nonperturbative test of the conjectural equivalence of the two theories in the conformal limit.