Conifolds with discrete torsion and noncommutativity

We study D3-branes at orbifolded conifold singularities in the presence of discrete torsion. The vacuum moduli space of open strings becomes non commu tative due to a deformation of the superpotential and is studied via the re presentation theory of the moduli algebra. It is also shown that the center of the moduli algebra correctly describes the underlying orbifolded conifo lds. The field theory can be obtained by a marginal deformation of the N = 1 gauge theory on D3-branes at conifold singularity, the global symmetry be ing broken from SU(2) X SU(2) to U(1) X U(1). By using the AdS/CFT correspo ndence we argue that the marginal deformation is related to massless KK mod es of NSNS and RR two form reduced on the compact space T-1,T-1. We build a T-2 fibration of T-1,T-1 and show that a D3-brane in the bulk correspond t o a D5-brane on the T-2 fibre. We also discuss the possible brane construct ion of the system.