{\cal N}=4 Supersymmetric Yang-Mills Theory on Orbifold-$T^4/{\bf Z}_2$: Higher Rank Case

TL;DR

This paper computes the partition function of { m N}=4 supersymmetric Yang-Mills theory on orbifold T^4/Z_2 for SU(N), extending previous SU(2) results to higher rank groups using advanced mathematical formulas.

Contribution

It generalizes the partition function calculation from SU(2) to SU(N) on orbifold T^4/Z_2, incorporating G"ottsche and blow-up formulas with A_{N-1} theta series.

Findings

Partition function expressed as a sum involving G"ottsche formula and blow-up formulas.

Extension from SU(2) to SU(N) case.

Inclusion of A_{N-1} theta series with level N.

Abstract

We derive the partition function of {\cal N}=4 supersymmetric Yang-Mills theory on orbifold-T^4/{\bf Z}_2 for gauge group SU(N). We generalize the method of our previous work for the SU(2) case to the SU(N) case. The resulting partition function is represented as the sum of the product of G\"ottche formula of singular quotient space $T^4/{\bf Z}_2 $ and of blow-up formulas including A_{N-1} theta series with level N.