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-commutative due to a deformation of the superpotential and is studied via the representation theory of the moduli algebra. It is also shown that the center of the moduli algebra correctly describes the underlying orbifolded conifolds. The field theory can be obtained by a marginal deformation of the ${\cal N} = 1$ gauge theory on D3 branes at conifold singularity, the global symmetry being broken from $SU(2) \times SU(2)$ to $U(1) \times U(1)$. By using the AdS/CFT correspondence we argue that the marginal deformation is related to massless KK modes of NSNS and RR two form reduced on the compact space $T^{1,1}$. We build a $T^2$ fibration of $T^{1,1}$ and show that a D3 brane in the bulk correspond to a D5 brane on the $T^2$ fibre. We also discuss the possible brane construction of the system.