Elaborations on the String Dual to N=1 SQCD

TL;DR

This work extends the string-dual description of a minimally SUSY SQCD-like theory by introducing new Type A backreacted backgrounds and validating their nonperturbative physics against field-theoretic expectations. It shows Seiberg duality is encoded geometrically as an exchange of internal cycles, reproduces gauge-coupling running and anomalous dimensions, and provides concrete predictions for Wilson and t'Hooft loops, the quartic coupling, and anomaly matching. The analysis reveals a smooth interpolation between Higgsed and confining vacua and connects UV and IR behaviors through controlled expansions and numerics, including a consistent flow across the $N_f=2N_c$ boundary. Together, these results strengthen the holographic understanding of SQCD-like dynamics and suggest precise avenues for connecting string backgrounds to realistic gauge theories.

Abstract

In this paper we make further refinements to the duality proposed between N=1 SQCD and certain string (supergravity plus branes) backgrounds, working in the regime of comparable large number of colors and flavors. Using the string theory solutions, we predict different field theory observables and phenomena like Seiberg duality, gauge coupling and its running, the behavior of Wilson and 't Hooft loops, anomalous dimensions of the quark superfields, quartic superpotential coupling and its running, continuous and discrete anomaly matching. We also give evidence for the smooth interpolation between higgsed and confining vacua. We provide several matchings between field theory and string theory computations.

Figures (6)

• Figure 1: We represent here the relationship between $C$ and $h_1$ that ensures that the evolution of a given type II expansion goes asymptotically to the behaviour we presented in section \ref{['sec: UV']}. On the left we are considering negative values of $C$, corresponding to expansion (\ref{['type II neg']}) while on the right positive values are considered, which correspond to (\ref{['type II pos']}). Dashed lines correspond to $\frac{N_f}{N_c}=1.5$ while continuous lines correspond to $\frac{N_f}{N_c}=2.5$.
• Figure 2: Type I solutions obtained numerically. We have fixed $C=0$, $N_c=1$ and defined $\rho=0$ as the point where $H$ ($G$) reaches a minimum for $N_f <2N_c$ ($N_f > 2N_c$). We plot the solutions for different values of $\frac{N_f}{N_c}$: dotted, dashed, dot-dashed and continuous lines correspond respectively to $N_f=1.2$, $1.8$, $2.2$, $3$$N_c$.
• Figure 3: Type II solutions derived numerically. In these plots we present the results for $C=-1$ and different values of $\frac{N_f}{N_c}$: dotted, dashed, dot-dashed and continuous lines correspond respectively to $N_f=1.2$, $1.8$, $2.2$, $3$$N_c$. The graphs on the left-hand side represent the solutions for the background on a large range of $\rho$, while the plots on the right-hand column focus on the behaviour of the functions close to the origin. Tilded function are rescaled by $N_c$ as $\tilde{H} = \frac{H}{N_c}$, etc.
• Figure 4: Type II and III solutions derived numerically. In these plots we present the behaviour of type III solutions, and compare it with small-$C$ type II solutions. Clearly the transition through $C=0$ is almost continuous. Here we have fixed $N_f=1.5 N_c$. Dotted lines correspond to the type III solution, while dot-dashed and continuous lines correspond to type II backgrounds with respectively $C=-0.1$ and $C=0.1$.
• Figure 5: These plots represent the behaviour of the gauge coupling as defined in equation (\ref{['esta']}) in type II (top) and type III (bottom) backgrounds. For the top plots we have taken $C=-1$ and different values of $\frac{N_f}{N_c}$. The correspondence between line styles and $\frac{N_f}{N_c}$ is the same as in figure \ref{['fig: type II C<0']}. For the bottom plots, we have taken $N_f=1.5 N_c$ and $C=-0.1$ and $0.1$ (type II), and $C=0$ (type III). For the correspondence between values of $C$ and line styles we refer the reader to the legend of figure \ref{['fig: type III']}. The plots on the right are a zoom around $\rho=0$ of the plots on the left.