Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-07-20
Physics
High Energy Physics
High Energy Physics - Theory
18 pages, 10 figures
Scientific paper
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.
Barranco Alejandro
Pallante Elisabetta
Russo Jorge G.
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