S-Duality in N=4 Yang-Mills Theories with General Gauge Groups,

TL;DR

This paper extends 't Hooft's construction to N=4 supersymmetric Yang-Mills theories with arbitrary gauge groups, analyzing fluxes and partition functions to verify S-duality transformations and provide evidence for the duality.

Contribution

It generalizes the analysis of S-duality to theories with arbitrary gauge groups and verifies the duality through exact computations of partition functions.

Findings

Partition function obeys S-duality transformation laws.

Exact leading infrared divergence computed for specific boundary conditions.

Provides independent evidence supporting S-duality in N=4 theories.

Abstract

't Hooft construction of free energy, electric and magnetic fluxes, and of the partition function with twisted boundary conditions, is extended to the case of $N=4$ supersymmetric Yang-Mills theories based on arbitrary compact, simple Lie groups. The transformation of the fluxes and the free energy under S-duality is presented. We consider the partition function of $N=4$ for a particular choice of boundary conditions, and compute exactly its leading infrared divergence. We verify that this partition function obeys the transformation laws required by S-duality. This provides independent evidence in favor of S-duality in $N=4$ theories.