Semi-classical Quantization in N=4 Supersymmetric Yang-Mills Theory and Duality

TL;DR

This paper explores semi-classical quantization and duality in N=4 supersymmetric Yang-Mills theory, analyzing monopole interactions and testing S-duality at various points in the moduli space.

Contribution

It provides a new perspective on monopole interactions and offers a simplified method to test S-duality in N=4 supersymmetric gauge theories.

Findings

Higgs and magneto-static forces do not cancel generically in the moduli space.

The moduli space of magnetic monopoles relates to the SU(2) case, simplifying duality tests.

Certain subspaces exhibit force cancellation, complicating S-duality verification.

Abstract

At a generic point in the moduli space of vacua of an N=4 supersymmetric gauge theory with arbitrary gauge group the Higgs force does not cancel the magneto-static force between magnetic monopoles of distinct charge. As a consequence the moduli space of magnetically charged solutions is related in a simple way to those of the SU(2) theory. This leads to a rather simple test of S-duality. On certain subspaces of the moduli space of vacua the forces between distinct monopoles cancel and the test of S-duality becomes more complicated.