N=1 SQCD-like theories with N_f massive flavors from AdS/CFT and beta functions

TL;DR

This paper constructs supergravity solutions for large-$N_c$ supersymmetric gauge theories with massive flavors, revealing different IR and UV behaviors and fixed points depending on the ratio of flavors to colors.

Contribution

It introduces a framework for solutions with massive flavors in supergravity, analyzing their IR and UV limits and fixed points, and explores Seiberg duality in this context.

Findings

For $x<2$, the beta function is negative and approaches the NSVZ form.

At $x=2$, a UV fixed point at strong coupling suggests an IR fixed point.

Solutions with $x>2$ relate to Seiberg duality, with sign flips in $N_f-2N_c$.

Abstract

We study new supergravity solutions related to large-$N_c$ ${\cal N}=1$ supersymmetric gauge field theories with a large number $N_f$ of massive flavors. We use a recently proposed framework based on configurations with $N_c$ color D5 branes and a distribution of $N_f$ flavor D5 branes, governed by a function $N_f S(r)$. Although the system admits many solutions, under plausible physical assumptions the relevant solution is uniquely determined for each value of $x\equiv N_f/N_c$. In the IR region, the solution smoothly approaches the deformed Maldacena-N\'u\~nez solution. In the UV region it approaches a linear dilaton solution. For $x<2$ the gauge coupling $\beta_g $ function computed holographically is negative definite, in the UV approaching the NSVZ $\beta $ function with anomalous dimension $\gamma_0= -1/2$ (approaching $-3/(32\pi^2)(2N_c-N_f)g^3$)), and with $\beta_g \to-\infty $ in the IR. For $x=2$, $\beta_g$ has a UV fixed point at strong coupling, suggesting the existence of an IR fixed point at a lower value of the coupling. We argue that the solutions with $x>2$ describe a "Seiberg dual" picture where $N_f-2N_c$ flips sign.