Comments on the String dual to N=1 SQCD

TL;DR

The paper develops a unified string-theory framework for N=1 SQCD with a quartic quark superpotential by comparing and extending Type A and Type N wrapped-brane backgrounds and deriving a master equation for the background function P. It uncovers new exact and asymptotic solutions, clarifies UV and IR behaviors, and provides a concrete RG-flow interpretation of the BPS equations, including a resolution of a beta-function puzzle and a screening criterion for Wilson loops. The analysis encompasses both SU(Nc) and SO(Nc) gauge groups, yielding a spinor Wilson loop candidate via a D3 on RP^2 that remains un-screened, and highlights Seiberg-like dualities encoded in the gravitational system. The results illuminate non-perturbative phenomena such as flavor-group enhancements, domain-wall tensions, and oblique confinement, with potential implications for holographic QCD and beyond-Standard-Model scenarios. Overall, the work delivers a coherent, technically detailed portrait of the string duals to N=1 SQCD and opens avenues for incorporating massive flavors and broader dualities.

Abstract

We study the String dual to N=1 SQCD deformed by a quartic superpotential in the quark superfields. We present a unified view of the previous results in the literature and find new exact solutions and new asymptotic solutions. Then we study the Physics encoded in these backgrounds, giving among other things a resolution to an old puzzle related to the beta function and a sufficient criteria for screening. We also extend our results to the SO(Nc) case where we present a candidate for the Wilson loop in the spinorial representation. Various aspects of this line of research are critically analyzed.

Figures (3)

• Figure 1: We represent the flow in the $(p,q)$ plane at fixed $u$ and $\tau=0$ (type A solutions). The physical region is above the black lines $p=\pm q >0$. (a) The RG flow for $N_c< N_f< 2N_c$. The $p'=0$ line (red) acts as an attractor for the flow, the dark lines are the limits of the attractor region $h'=0$ and $g'=0$. The $u'=0$ line (blue) has also been represented. (b) The RG flow for $N_f=2N_c$. The $p'=0$ (red) and $u'=0$ (blue) lines have been represented. There are two fixed points of the flow at the intersection of the two curves.
• Figure 2: The tension of the D3 brane wrapping a $RP^2$ cycle has a minimum as a function of $\rho$ for the three types of A backgrounds, so the holographic dual object is not screened in any of them.
• Figure 3: Diagram for a meson propagator, with two insertions of the meson operator ($n=2$) shown as thick points on the boundaries. The dashed lines are gluons that fill the diagram in the large $N_c$ limit and the thick lines are quarks. A) Planar diagram with no internal quark loops ($h=0$, $w=0$), the scaling is $\sim 1$. B) Planar diagram with an internal quark loop $h=0$, $w=1$, the scaling is $\sim N_f/N_c$. C) Non-planar diagram with no internal quark loops $h=0$, $w=0$, $b=2$, the scaling is $\sim 1/N_c$.