Instanton Effects in Supersymmetric Yang-Mills Theories on ALE Gravitational Backgrounds

TL;DR

This paper computes instanton-dominated correlation functions in supersymmetric Yang-Mills theories on ALE gravitational backgrounds, explicitly constructing self-dual connections on ALE spaces, focusing on the Eguchi-Hanson case.

Contribution

It provides explicit construction of self-dual connections on ALE spaces for supersymmetric Yang-Mills theories, enabling instanton effect calculations on these gravitational backgrounds.

Findings

Explicit construction of self-dual connections on ALE spaces.

Calculation of instanton-dominated correlation functions.

Application to the Eguchi-Hanson gravitational background.

Abstract

In this letter we report on the computation of instanton-dominated correlation functions in supersymmetric YM theories on ALE spaces. Following the approach of Kronheimer and Nakajima, we explicitly construct the self-dual connection on ALE spaces necessary to perform such computations. We restrict our attention to the simplest case of an $SU(2)$ connection with lowest Chern class on the Eguchi-Hanson gravitational background.