Supersymmetry and the Multi-Instanton Measure II: From N=4 to N=0

TL;DR

This paper derives explicit formulas for the multi-instanton measure in N=4 supersymmetric SU(2) gauge theory and extends these results to the non-supersymmetric case, connecting different supersymmetry levels.

Contribution

It provides an explicit formula for the multi-instanton measure in N=4 supersymmetric gauge theory and relates it to lower supersymmetry cases, including the non-supersymmetric limit.

Findings

Derived explicit multi-instanton measure for N=4 supersymmetry.

Established a renormalization group relation between N=4, N=2, and N=1 measures.

Constructed the classical N=0 measure without one-loop fluctuations.

Abstract

Extending recent N=1 and N=2 results, we propose an explicit formula for the integration measure on the moduli space of charge-n ADHM multi-instantons in N=4 supersymmetric SU(2) gauge theory. As a consistency check, we derive a renormalization group relation between the N=4, N=2, and N=1 measures. We then use this relation to construct the purely bosonic (``N=0'') measure as well, in the classical approximation in which the one-loop small-fluctuations determinants is not included.