An Approach to ${\cal N}=4$ ADE Gauge Theory on K3

TL;DR

This paper generalizes the calculation of the partition function for ${ m N}=4$ $ADE$ gauge theories on K3 surfaces, demonstrating that the resulting functions satisfy Montonen-Olive duality, extending previous SU(N) results.

Contribution

It introduces a new method to compute partition functions for ${ m N}=4$ $ADE$ gauge theories on K3, confirming duality properties for these groups.

Findings

Partition function formula for ${ m N}=4$ $ADE$ gauge theories on K3.

Verification of Montonen-Olive duality for these theories.

Extension of previous SU(N) results to ADE gauge groups.

Abstract

We propose a recipe for determination of the partition function of ${\cal N}=4$ $ADE$ gauge theory on $K3$ by generalizing our previous results of the SU(N) case. The resulting partition function satisfies Montonen-Olive duality for $ADE $ gauge group.