Holographic duals of flavored Script N = 1 super Yang-Mills: beyond the probe approximation

We construct backreacted D3/D7 supergravity backgrounds which are dual to four-dimensional Script N = 1 and Script N = 2 supersymmetric Yang-Mills at large N_c with flavor quarks in the fundamental representation of SU(N_c). We take into account the backreaction of D7-branes on either AdS₅ × S⁵ or AdS₅ × T^1,1, or more generically on backgrounds where the space transverse to the D3-branes is Kähler. The construction of the backreacted geometry splits into two stages. First we determine the modification of the six-dimensional space transverse to the D3 due to the D7, and then we compute the warp factor due to the D3. The Script N = 2 background corresponds to placing a single stack of N_f D7-branes in AdS₅ × S⁵. Here the Kähler potential is known exactly, while the warp factor is obtained in certain limits as a perturbative expansion. By placing another D7' probe in the backreacted D3/D7 background, we derive the effect of the D7-branes on the spectrum of the scalar fluctuations to first order in N_f. The two systems with Script N = 1 supersymmetry that we discuss are D3/D7/D7' and D3/D7 on the conifold. In both cases, the Kähler potential is obtained perturbatively in the number of D7-branes. We provide all the ingredients necessary for the computation of each term in the expansion, and in each case give the first few terms explicitly. Finally, we comment on some aspects of the dual gauge theories.