DYONS AND S-DUALITY IN N=4 SUPERSYMMETRIC GAUGE-THEORY

We analyze the spectrum of dyons in N = 4 supersymmetric Yang-Mills th eory with gauge group SU(3) spontaneously broken down to U(1) x U(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 obt ained by embedding SU(2) monopoles into SU(3) and the S-duality predic tions reduce to the SU(2) case. Acting with S-duality on the W-boson c orresponding to a nonsimple root leads to an infinite set of new S-dua lity predictions. The simplest of these corresponds to the existence o f a harmonic form on the moduli space of SU(3) monopoles that have mag netic charge (1, 1) with respect to the two U(1)'s. We argue that the moduli space is given by R(3) x (R(1) x M)/Z, where M is Euclidean Tau b-NUT space, and that the latter admits the appropriate normalizable h armonic two-form. We briefly discuss the generalizations to other gaug e groups.