Holomorphic Yang-Mills Theory and Variation of the Donaldson Invariants

TL;DR

This paper investigates the holomorphic Yang-Mills theory on Kähler surfaces with specific topological properties, analyzing its path integrals, correlation functions, and their relation to Donaldson invariants.

Contribution

It provides new insights into the behavior of Donaldson invariants through the study of holomorphic Yang-Mills path integrals on Kähler surfaces with $b_2^+ = 1$.

Findings

Derived transition formulas for Donaldson invariants.

Analyzed correlation functions in topological Yang-Mills theory.

Connected holomorphic Yang-Mills path integrals to Donaldson invariants.

Abstract

We study the path integrals of the holomorphic Yang-Mills theory on compact K\"{a}hler surface with $b_2^+ = 1$. Based on the results, we examine the correlation functions of the topological Yang-Mills theory and the corresponding Donaldson invariants as well as their transition formulas.