Instanton Counting and Localization

Abstract

The aim of this Chapter is to introduce the Yang–Mills (YM) theory, and explain how the specific solution, called the instanton, plays an important role in four-dimensional gauge theory. We will explain a systematic method to describe the instanton solution, a.k.a. ADHM construction [2], and discuss how the moduli space of the instanton plays a role in the path integral formalism of the YM theory. In particular, volume of the instanton moduli space is an important quantity, but we should regularize it due to the singular behavior of the moduli space. We will then consider the equivariant action on the instanton moduli space, and apply the equivariant localization scheme to evaluate the volume of the moduli space [1, 7, 9], which gives rise to the instanton partition function [26, 27, 30, 37, 38].