Gauge-gravity duals with a holomorphic dilaton

We consider configurations of D7-branes and whole and fractional D3-branes with $\mathcal{N}=2\mathrm{}$ supersymmetry. On the supergravity side these have a warp factor, three-form flux and a nonconstant dilaton. We discuss general type IIB solutions of this type and then obtain the specific solutions for the D7-D3 system. On the gauge side the D7-branes add matter in the fundamental representation of the D3-brane gauge theory. We find that the gauge and supergravity metrics on moduli space agree. However, in many cases the supergravity curvature is large even when the gauge theory is strongly coupled. In these cases we argue that the useful supergravity dual must be a type IIA configuration.