Conifolds with discrete torsion and noncommutativity

We study D3 branes at orbifolded conifold singularities in the presence ofdiscrete torsion. The vacuum moduli space of open strings becomesnon-commutative due to a deformation of the superpotential and is studied viathe representation theory of the moduli algebra. It is also shown that thecenter of the moduli algebra correctly describes the underlying orbifoldedconifolds. The field theory can be obtained by a marginal deformation of the${\cal N} = 1$ gauge theory on D3 branes at conifold singularity, the globalsymmetry being broken from $SU(2) \times SU(2)$ to $U(1) \times U(1)$. By usingthe AdS/CFT correspondence we argue that the marginal deformation is related tomassless 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 inthe bulk correspond to a D5 brane on the $T^2$ fibre. We also discuss thepossible brane construction of the system.Comment: Latex, 24 pages, v2: small change