AnN=1 duality cascade from a deformation ofN=4 SUSY Yang-Mills

We study relevant deformations of an N=1 superconformal theory which is anexactly marginal deformation of U(N) N=4 SUSY Yang-Mills. The resulting theoryhas a classical Higgs branch that is a complex deformation of the orbifoldC^3/Z_n x Z_n that is a non-compact Calabi-Yau space with isolated conifoldsingularities. At these singular points in moduli space the theory exhibits aduality cascade and flows to a confining theory with a mass gap. By exactlysolving the corresponding holomorphic matrix model we compute the exact quantumsuperpotential generated at the end of the duality cascade and calculateprecisely how quantum effects deform the classical moduli space by replacingthe conifold singularities with three-cycles of finite size. Locally thestructure is that of the deformed conifold, but the global geometry isdifferent. This desingularized quantum deformed geometry is the moduli space ofprobe D3-branes at the end of a duality cascade realized on the worldvolume of(fractional) D3-branes placed at the isolated conifold singularities in thedeformation of the orbifold C^3/Z_n x Z_n with discrete torsion.Comment: Uses Latex, JHEP.cls, 43 pages, 3 figure