Holomorphic Yang-Mills Theory on Compact K\"{a}hler Manifolds

TL;DR

This paper introduces an $N=2$ holomorphic Yang-Mills theory on compact Kähler manifolds, linking it to topological Yang-Mills theory and enabling the computation of intersection pairings via small coupling analysis.

Contribution

It generalizes Witten's two-dimensional Yang-Mills work to higher dimensions using holomorphic structures on Kähler manifolds.

Findings

Establishes a mapping between $N=2$ holomorphic and topological Yang-Mills theories.

Shows intersection pairings can be derived from small coupling behavior.

Provides a higher-dimensional framework for Yang-Mills theory on Kähler manifolds.

Abstract

We propose $N=2$ holomorphic Yang-Mills theory on compact K\"{a}hler manifolds and show that there exists a simple mapping from the $N=2$ topological Yang-Mills theory. It follows that intersection parings on the moduli space of Einstein-Hermitian connections can be determined by examining the small coupling behavior of the $N=2$ holomorphic Yang-Mills theory. This paper is a higher dimensional generalization of the Witten's work on physical Yang-Mills theory in two dimensions.