Holographic Duals of Flavored N=1 Super Yang-Mills: Beyond the Probe Approximation

TL;DR

This paper constructs backreacted supergravity backgrounds dual to flavored N=1 and N=2 supersymmetric Yang-Mills theories, going beyond the probe approximation by including the effects of flavor branes on the geometry.

Contribution

It develops a method to incorporate D7-brane backreaction into supergravity backgrounds for N=1 and N=2 theories, providing explicit perturbative solutions and spectrum analysis.

Findings

Backreacted geometries for N=2 and N=1 supersymmetric theories constructed.

Perturbative expansion of the Kaehler potential and warp factor obtained.

Effect of flavor branes on scalar fluctuation spectrum analyzed.

Abstract

We construct backreacted D3/D7 supergravity backgrounds which are dual to four-dimensional N=1 and 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 AdS(5) x S(5) or AdS(5) x T^{1,1}, or more generically on backgrounds where the space transverse to the D3-branes is Kaehler. 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 N=2 background corresponds to placing a single stack of N_f D7-branes in AdS(5) x S(5). Here the Kaehler 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 N=1 supersymmetry that we discuss are D3/D7/D7' and D3/D7 on the conifold. In both cases, the Kaehler 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.