Instantons, Compactification and S-duality in N=4 SUSY Yang-Mills Theory I

TL;DR

This paper derives exact formulas for the effective action in N=4 SU(2) SYM compactified to three dimensions, revealing SL(2,Z) duality invariance and providing insights into instanton effects in gauge and string theories.

Contribution

It provides the first exact determination of eight fermion terms in the effective action for all circle sizes, assuming a Spin(8) fixed point, demonstrating duality invariance.

Findings

Exact formulas for fermion terms invariant under SL(2,Z)

Predictions for instanton effects in gauge and string theories

Insights into the structure of N=4 SYM on compactified spaces

Abstract

We study N=4 supersymmetric Yang-Mills (SYM) theory with gauge group SU(2) compactified to three dimensions on a circle of circumference beta. The eight fermion terms in the effective action on the Coulomb branch are determined exactly, for all beta, assuming the existence of an interacting Spin(8) invariant fixed point at the origin. The resulting formulae are manifestly invariant under the SL(2,Z) duality of four dimensional N=4 SYM and lead to interesting quantitative predictions for instanton effects in gauge theory and in Type II string theory.