Deformation of Dijkgraaf-Vafa relation via spontaneously broken N=2 supersymmetry II

We consider the matter induced part of the effective superpotential of N=2, U(N) gauge model in which N=2 supersymmetry is spontaneously broken to N=1, by using the properties of the chiral ring and the generalized Konishi anomaly equations derived in our previous paper [H. Itoyama, K. Maruyoshi, Phys. Lett. B 650 (2007) 298, arXiv: 0704.1060 [hep-th]]. It is shown that the effective superpotential is related to the planar free energy of the matrix model by a formula which consists of two parts-the well-known part due to Dijkgraaf-Vafa and the part that acts as a deformation of the couplings. These couplings are those of the original bare prepotential in the action and at the same time matrix model couplings.