N=4 Supersymmetric Yang-Mills Theory on a Kaehler Surface

TL;DR

This paper investigates N=4 supersymmetric Yang-Mills theory on Kaehler surfaces, revealing that its partition function decomposes into instanton and Seiberg-Witten monopole contributions, and derives a formula for the Euler characteristic of instanton moduli spaces.

Contribution

It demonstrates the decomposition of the partition function into two branches and computes it explicitly for SU(2) and SO(3) gauge groups using S-duality.

Findings

Partition function splits into instanton and monopole contributions.

Derived a formula for the Euler characteristic of instanton moduli spaces.

Applied S-duality to compute partition functions for specific gauge groups.

Abstract

We study N=4 supersymmetric Yang-Mills theory on a Kaehler manifold with $b_2^+ \geq 3$. Adding suitable perturbations we show that the partition function of the N=4 theory is the sum of contributions from two branches: (i) instantons, (ii) a special class of Seiberg-Witten monopoles. We determine the partition function for the theories with gauge group SU(2) and SO(3), using S-duality. This leads us to a formula for the Euler characteristic of the moduli space of instantons.