Holographic flavour in the N=1 Polchinski-Strassler background

To endow the N =1* SYM theory with quarks, we embed D7-brane probes into its gravity dual, known as the Polchinski-Strassler background. The non-vanishing 3-form flux G(3) in the background is dual to mass terms for the three adjoint chiral superfields, deforming the N = 4 SYM theory to the N = 1* SYM theory. We keep its three mass parameters independent. This generalizes our analysis in hep-th/0610276 for the N= 2* SYM theory. We work at second order in the mass perturbation, i.e. G(3) and its backreaction on the background are considered perturbatively up to this order. We find analytic solutions for the embeddings which in general depend also on angular variables. We discuss the properties of the solutions and give error estimates on our approximation. By applying the method of holographic renormalization, we show that in all cases the embeddings are at least consistent with supersymmetry.