D3-D7 background and flavor dependence of Regge trajectories

In the context of AdS/CFT with flavor, we consider the type IIB supergravity solution corresponding to a fully localized D3/D7 intersection. We complete the standard metric ansatz by providing an analytic expression for the warp factor, under the assumption of a logarithmically running axion-dilaton. From the gauge dual perspective, this behavior is related to the positive beta function of the N=4, d=4 SU(N-c) super Yang-Mills gauge theory, coupled to N-f fundamental N=2 hypermultiplets. We comment on the existence of tadpoles and relate them to the same gauge theory beta function. Next we consider a classical spinning string configuration in the decoupling limit of the D3/D7 geometry and extract the flavor (N-f) dependence of the associated meson Regge trajectory. Including the backreaction of the D7-branes in the supergravity dual allows for going beyond the quenched approximation on the dual gauge theory side.