  In this note we show how Dijkgraaf and Vafa's hypothesis relating the exact
superpotential of an N=1 theory to a matrix model can be used to describe all
the massive vacua of the N=1*, or mass deformed N=4, theory including the Higgs
vacuum. The matrix model computation of the superpotential for each massive
vacuum independently yields a modular function of the associated effective
coupling in that vacuum which agrees with previously derived results up to a
vacuum-independent additive constant. The results in the different massive
vacua can be related by the action of SL(2,Z) on the N=4 coupling, thus
providing evidence for modular invariance of the underlying N=4 theory.
