Dyons and S-Duality in N=4 Supersymmetric Gauge Theory

TL;DR

This paper explores the spectrum of dyons in N=4 supersymmetric Yang-Mills theory with gauge group SU(3), demonstrating how S-duality predicts new dyon states and analyzing their mathematical structure and moduli space.

Contribution

It provides a detailed analysis of dyon spectra in SU(3) gauge theory under S-duality, including the construction of monopole solutions and the harmonic forms on their moduli space.

Findings

S-duality generates an orbit of BPS dyon states from W-bosons.

The moduli space of monopoles is modeled as R^3x(R^1xM)/Z_2, with M as Euclidean Taub-NUT space.

Existence of a harmonic form on the monopole moduli space supports S-duality predictions.

Abstract

We analyze the spectrum of dyons in N=4 supersymmetric Yang-Mills theory with gauge group SU(3) spontaneously broken down to U(1)xU(1). The Higgs fields select a natural basis of simple roots. Acting with S-duality on the W-boson states corresponding to simple roots leads to an orbit of BPS dyon states that are magnetically charged with respect to one of the U(1)'s. The corresponding monopole solutions can be obtained by embedding SU(2) monopoles into SU(3) and the S-duality predictions reduce to the SU(2) case. Acting with S-duality on the W-boson corresponding to a non-simple root leads to an infinite set of new S-duality predictions. The simplest of these corresponds to the existence of a harmonic form on the moduli space of SU(3) monopoles that have magnetic charge (1,1) with respect to the two U(1)'s. We argue that the moduli space is given by R^3x(R^1xM)/Z_2, where M is Euclidean Taub-NUT space, and that the latter admits the appropriate normalizable harmonic two form. We briefly discuss the generalizations to other gauge groups.