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

TL;DR

This paper derives the partition function of N=4 supersymmetric Yang-Mills theory on an orbifolded four-torus, connecting it to the geometry of K3 surfaces through orbifold construction and blow-up formulas.

Contribution

It provides a novel derivation of the partition function on orbifold-$T^4/{f Z}_2$, linking gauge theory to geometric structures of K3 surfaces.

Findings

Partition function expressed as product of untwisted and twisted sector contributions.

Connection established between orbifold construction and K3 surface geometry.

Utilization of blow-up formulas for ${ m O}(-2)$ curves.

Abstract

We derive the partition function of N=4 supersymmetric Yang-Mills theory on orbifold-$T^4/{\bf Z}_2$. In classical geometry, K3 surface is constructed from the orbifold-$T^4/{\bf Z}_2$. Along the same way as the orbifold construction, we construct the partition function of K3 surface from orbifold-$T^4/{\bf Z}_2$. The partition function is given by the product of the contribution of the untwisted sector of $T^4/{\bf Z}_2$, and that of the twisted sector of $T^4/{\bf Z}_2$ i.e., ${\cal O}(-2)$ curve blow-up formula.