3D-partition functions on the sphere: exact evaluation and mirror symmetry

TL;DR

This paper computes exact 3D partition functions for N=4 quiver theories on the sphere, revealing explicit formulas and supporting mirror symmetry through non-perturbative checks, advancing understanding of these theories and their duals.

Contribution

It provides exact formulas for partition functions of N=4 quiver theories, including the T(SU(N)) tail and TN theories, facilitating analysis of mirror symmetry and star-shaped quivers.

Findings

Exact partition function formula for T(SU(N)) quiver tail.

Non-perturbative verification of mirror symmetry.

Partition functions for TN theories as fundamental building blocks.

Abstract

We study N = 4 quiver theories on the three-sphere. We compute partition functions using the localisation method by Kapustin et al. solving exactly the matrix integrals at finite N, as functions of mass and Fayet-Iliopoulos parameters. We find a simple explicit formula for the partition function of the quiver tail T(SU(N)). This formula opens the way for the analysis of star-shaped quivers and their mirrors (that are the Gaiotto-type theories arising from M5 branes on punctured Riemann surfaces). We provide non-perturbative checks of mirror symmetry for infinite classes of theories and find the partition functions of the TN theory, the building block of generalised quiver theories.