  The Dijkgraaf-Vafa approach is used in order to study the Coulomb branch of
the Leigh-Strassler massive deformation of N=4 SYM with gauge group U(N). The
theory has N=1 SUSY and an N-dimensional Coulomb branch of vacua, which can be
described by a family of ``generalized'' Seiberg-Witten curves. The matrix
model analysis is performed by adding a tree level potential that selects
particular vacua. The family of curves is found: it consists of order N
branched coverings of a base torus, and it is described by multi-valued
functions on the latter. The relation between the potential and the vacuum is
made explicit. The gauge group SU(N) is also considered. Finally the resolvents
from which expectation values of chiral operators can be extracted are
presented.
