Supersymmetric Yang-Mills Theory On A Four-Manifold

TL;DR

This paper demonstrates how supersymmetric Yang-Mills theory can be used to compute Donaldson invariants of four-manifolds with Kahler metrics, confirming mathematical results and validating theoretical predictions.

Contribution

It provides a novel method to compute Donaldson invariants using supersymmetric Yang-Mills theory on four-manifolds with Kahler metrics, aligning physics with mathematics.

Findings

Results agree with existing mathematical computations.

Validates supersymmetric Yang-Mills theory as a tool for topological invariants.

Shows consistency of physical and mathematical approaches.

Abstract

By exploiting standard facts about $N=1$ and $N=2$ supersymmetric Yang-Mills theory, the Donaldson invariants of four-manifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about supersymmetric Yang-Mills theory.