On the Multi-Instanton Measure for Super Yang--Mills Theories

TL;DR

This paper revisits the derivation of the multi-instanton measure in supersymmetric Yang-Mills theories, generalizing the moduli space construction to supermanifolds and providing explicit computations for N=2 theories.

Contribution

It introduces a supermanifold-based construction of the multi-instanton measure, extending the hyperkähler quotient approach to supersymmetric gauge theories.

Findings

Explicit supermoduli space construction for N=2 theories

Derivation of the supermetric for the instanton measure

Generalization of the hyperkähler quotient to supermanifolds

Abstract

In this paper we revisit the arguments that have led to the proposal of a multi-instanton measure for supersymmetric Yang-Mills theories. We then recall how the moduli space of gauge connections on $\real^4$ can be built from a hyperk\"ahler quotient construction which we generalize to supermanifolds. The measure we are looking for is given by the supermetric of the supermoduli space thus introduced. To elucidate the construction we carry out explicit computations in the case of N=2 supersymmetric Yang-Mills theories.