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

TL;DR

This work constructs fully backreacted D3/D7 backgrounds as holographic duals of 4D $N=1$ and $N=2$ SYM with fundamental flavors at large $N_c$, going beyond the probe approximation by solving for the Kaehler geometry of the six-dimensional space transverse to the D3 and then determining the D3 warp factor.The methodology splits the problem into a Monge-Ampère type equation for the Kaehler potential and a separate harmonic equation for the warp factor, enabling perturbative solutions in the number of D7 branes for configurations with one or two stacks and for conifold embeddings.Key results include explicit perturbative Kaehler potentials for D3/D7 and D3/D7/D7′ systems, a perturbative spectrum for scalar mesons on a backreacted background, and two embeddings of D7-branes on the conifold (w4 = 0 and a P1-inspired patch) with corresponding backreaction analyses.The work also discusses gauge-theory implications, including the role of the dilaton in running couplings and beta functions, and identifies pathologies such as naked singularities and Landau poles that constrain the holographic regime, outlining several open directions for future research.

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.