Non-planar diagrams and non-commutative superspace in Dijkgraaf-Vafa theory

We consider the field theory on non-commutative superspace and non-commutative spacetime that arises on D-branes in Type II superstring theory with a constant self-dual graviphoton and NS-NS B field background. N=1 supersymmetric field theories on this non-commutative space (such theories are called N=1/2 supersymmetric theories) can be reduced to supermatrix models as in hep-th/0303210. We take an appropriate commutative limit in these theories and show that holomorphic quantities in commutative field theories are equivalent to reduced models, including non-planar diagrams to which the graviphoton contributes. This is a new derivation of Dijkgraaf-Vafa theory including non-planar diagrams