Towards the String Dual of N=1 SQCD-like Theories

TL;DR

The paper develops gravity duals for ${ m N}=1$ SQCD-like theories by adding backreacting flavor branes to wrapped D5-brane backgrounds, enabling a holographic study of nonperturbative dynamics at ${N_f\sim N_c}$. It derives flavored BPS equations, analyzes IR/UV behavior, and extracts gauge-theory predictions such as Wilson loops with pair creation, instanton actions, $U(1)_R$ breaking, and Seiberg duality via dual geometric descriptions; it also examines a special ${N_f=2N_c}$ case signaling an IR-like fixed point. A second track explores unflavored backgrounds with a UV completion, yielding a one-parameter family of deformations and rich phenomenology including confining strings, Rotating strings, PP-waves, and a NSVZ-like beta-function under caveats. Together, these results offer a concrete string-theoretic framework for SQCD-like dynamics, including the interplay between color, flavor, and KK modes, and provide qualitative predictions for nonperturbative phenomena amenable to further holographic checks. The work opens avenues toward non-supersymmetric extensions, finite-temperature dynamics, and explicit sigma-model realizations of strings in these backgrounds.

Abstract

We construct supergravity plus branes solutions, which we argue to be related to 4d N=1 SQCD with a quartic superpotential. The geometries depend on the ratio Nf/Nc which can be kept of order one, present a good singularity at the origin and are weakly curved elsewhere. We support our field theory interpretation by studying a variety of features like R-symmetry breaking, instantons, Seiberg duality, Wilson loops and pair creation, running of couplings and domain walls. In a second part of this paper, we address a different problem: the analysis of the interesting physics of different members of a family of supergravity solutions dual to (unflavored) N=1 SYM plus some UV completion.

Figures (5)

• Figure 1: Some functions of the flavored solutions for $N_f = 0.5 N_c$ (thin solid lines), $N_f=1.2 N_c$ (dashed lines), $N_f = 1.6 N_c$ (dotted lines). For comparison, we also plot (thick solid lines) the usual unflavored solution. The graphs are $e^{2k}$, $e^{2g}$, $e^{2h}$, $\phi$, $a$ and a zoom of the plot for $a$ near $\rho=0$. In the figures for $a$ we have also plotted with a light solid line $a=\frac{1}{\cosh (2\rho)}.$
• Figure 2: Energy vs. length of the Wilson loop for $\frac{N_f}{N_c}=0.2$ and $\frac{N_f}{N_c}=0.5$. Energies are in units of $\frac{e^{\phi_0}\sqrt{g_s N_c}}{\sqrt\alpha'}$, whereas lengths are in units of $\sqrt{g_s N_c \alpha'}$ .There is a value of the integration constant $\rho_0$ for which the string reaches its maximum $L$ and $E$. Longer strings are not solutions of the Nambu-Goto action. We interpret it as string breaking due to quark-antiquark pair creation.
• Figure 3: We plot the different functions for different values of the parameter $\mu$. The thick solid line corresponds to $\mu=-\frac{2}{3}$ (the usual MN case), the solid thin lines correspond, respectively, to $\mu=-.68,-1,-1.5$ and the dashed line is a deformed conifold.
• Figure 4: We plot the inverse 't Hooft coupling and $e^{\phi}$ for $\mu=-.67$ (thin line) compared with the usual $\mu=-\frac{2}{3}$ case (thick line). Starting from some value of $\rho$ ($\Lambda_{UV}$), the UV completion sets in and the geometry asymptotes to a (Ricci flat) conifold. $\Lambda_{UV}$ decreases as $\mu$ decreases.
• Figure 5: Behavior of the background functions for the $x=2$ solution with $a=\frac{1}{\cosh 2\rho}$. From the top left we have $e^{2k(\rho)}$, $e^{2h(\rho)}$, $e^{2g(\rho)}$, $e^{2(f(\rho)-f_0)}$. Here we have taken $N_c=1$.