Anisotropic D3-D5 black holes with unquenched flavors

We construct a black hole geometry generated by the intersection of $N_c$ color D3- branes and $N_f$ flavor D5-branes along a 2+1 dimensional subspace. Working in the Veneziano limit in which $N_f$ is large and distributing homogeneously the D5-branes in the internal space, we calculate the solution of the equations of motion of supergravity plus sources which includes the backreaction of the flavor branes. The solution is analytic and dual to a 2+1 dimensional defect in a 3+1 dimensional gauge theory, with $N_f$ massless hypermultiplets living in the defect. We study the thermodynamics of the resulting spatially anisotropic geometry and compute the first and second order transport coefficients for perturbations propagating along the defect.