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

TL;DR

This paper performs semiclassical calculations of instanton effects in N=4 and N=1 supersymmetric Yang-Mills theories on R^{3}XS^{1}, testing recent exact results related to BPS states and effective actions.

Contribution

It provides the first semiclassical verification of exact results for instanton contributions and BPS dyon indices in compactified N=4 SUSY Yang-Mills theory.

Findings

Instanton effects match predictions from exact formulas.

Calculations support the proposed dualities and index computations.

Results extend to N=1 theories with chiral multiplet masses.

Abstract

We present a semiclassical calculation of instanton effects in N=4 supersymmetric Yang-Mills theory formulated on R^{3}XS^{1} and also in the N=1 theory obtained by introducing chiral multiplet masses. In the N=4 case, these instanton effects are related to the bulk contribution to the index which counts BPS dyons in the corresponding four dimensional theory. In both cases, the calculations provide semiclassical tests of recently proposed exact results for the lowest non-trivial terms in the derivative expansion of the Wilsonian effective action.