N=2 Topological Yang-Mills Theory on Compact K\"{a}hler Surfaces

TL;DR

This paper explores a topological N=2 Yang-Mills theory on compact Kähler surfaces, linking it to Donaldson invariants and discussing localization techniques for potential applications.

Contribution

It provides a field theoretical framework for Donaldson invariants on Kähler surfaces and examines localization methods in this context.

Findings

Field theory interpretation of Donaldson invariants.

Application of localization formulas to Kähler surfaces.

Analysis of N=2 topological Yang-Mills on Riemann surfaces.

Abstract

We study a topological Yang-Mills theory with $N=2$ fermionic symmetry. Our formalism is a field theoretical interpretation of the Donaldson polynomial invariants on compact K\"{a}hler surfaces. We also study an analogous theory on compact oriented Riemann surfaces and briefly discuss a possible application of the Witten's non-Abelian localization formula to the problems in the case of compact K\"{a}hler surfaces.