Three-dimensional super Yang-Mills with unquenched flavor

Abstract

We construct analytically the gravity duals of three-dimensional, super Yang-Mills-type theories with $\mathcal N=1$ supersymmetry coupled to $N_f$ quark flavors. The backreaction of the quarks on the color degrees of freedom is included, and corresponds on the gravity side to the backreaction of $N_f$ D6-branes on the background of $N$ D2-branes. The D6-branes are smeared over the compact part of the geometry, which must be a six-dimensional nearly K\"ahler manifold in order to preserve supersymmetry. For massless quarks, the solutions flow in the IR to an $AdS_4$ fixed point dual to a Chern-Simons-matter theory. For light quarks the theories exhibit quasi-conformal dynamics (walking) at energy scales $m_q \ll E \ll \lambda N_f / N$, with $\lambda = g_{\text{YM}}^2 N$ the 't Hooft coupling.