D3-D5 theories with unquenched flavors

We construct the string duals of the defect theories generated when Nf flavor D5-branes intersect Nc color D3-branes along a 2+1 dimensional subspace. We work in the Veneziano limit in which Nc and Nf are large and Nf/Nc is fixed. By smearing the D5-branes, we find supergravity solutions that take into account the backreaction of the flavor branes and preserve two supercharges. When the flavors are massless the resulting metric displays an anisotropic Lifshitz-like scale invariance. The case of massive quarks is also considered.