Nonperturbative tests of three-dimensional dualities

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.

M5-branes from gauge theories on the 5-sphere

“…One thus finds that the perturbative part of the partition function, with 16 SUSY, takes the form of the pure Chern-Simons partition function on S 3 [24]. See also [25,26] for some later studies of the same expression.…”

Mirror theories of 3d $$ \mathcal{N} $$ = 2 SQCD

“…The matching of partition functions for many mirror theories in this class was checked analytically in [22,27].…”

ABJ theory in the higher spin limit

“…However, for the purpose of studying its HS limit, the most convenient starting point is the "mirror description" of the ABJ partition function found in [92], generalizing the mirror description of the ABJM partition function [106,107]. The "mirror description" of the ABJ partition function is as follows:…”