Flavor corrections to the entanglement entropy

We consider the holographic entanglement entropy in N=4 SYM coupled to massive flavor degrees of freedom. The flavors are introduced by putting D7 branes in AdS_5. The resulting geometry including the backreaction of the branes is known in a perturbation expansion in the ratio N_f/N_c. We consider the expansion to first order, and compute the entanglement entropy of a region of the boundary. We consider two different cases for the geometry of the region: a slab and a ball. We find analytic solutions for the minimal surfaces in the bulk whose area gives the entropy, and analyze the structure of the UV divergence and the dependence on the masses. Our results confirm the general structure that was predicted by free field theory calculations, but with coefficients that depend on the coupling.