Fractional branes and the gravity dual of partial supersymmetry breaking

In type IIB string theory, we consider fractional D3-branes in the orbifold background dual to four-dimensional N=2N=2 supersymmetric Yang–Mills theory. We find the gravitational dual description of the generation of a non-trivial field theory potential on the Coulomb branch. When the orbifold singularity is softened to the smooth Eguchi–Hanson space, the resulting potential induces spontaneous partial supersymmetry breaking. We study the N=1N=1 theory arising in those vacua and we see how the resolved conifold geometry emerges in this way. It will be natural to identify the size of the blown-up two-cycle of that geometry with the inverse mass of the adjoint chiral scalar. We finally discuss the issue of geometric transition in this context.