Nonperturbative Tests of Three-Dimensional Dualities

TL;DR

This paper performs nonperturbative tests of three-dimensional dualities by computing exact partition functions of superconformal theories on a three-sphere, confirming mirror symmetry and the equivalence of N=8 super-Yang-Mills and ABJM theories.

Contribution

It provides the first nonperturbative verification of dualities between strongly coupled 3D superconformal theories using localization techniques.

Findings

Partition functions of mirror theories agree when parameters are exchanged.

Partition functions of N=8 super-Yang-Mills and ABJM theories match at unit Chern-Simons level.

Supports the conjecture of dualities in three-dimensional superconformal field 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.