Three-dimensional super Yang-Mills with unquenched flavor

TL;DR

This paper constructs gravity duals for three-dimensional super Yang-Mills theories with unquenched flavors, revealing IR fixed points and quasi-conformal dynamics depending on quark mass, thus advancing holographic modeling of flavored gauge theories.

Contribution

It provides analytical gravity dual solutions for 3D super Yang-Mills theories with backreacted flavors, including massless and light quark regimes, with implications for IR fixed points and walking behavior.

Findings

Flow to an AdS4 fixed point in IR for massless quarks

Presence of quasi-conformal (walking) behavior for light quarks

Backreaction of smeared D6-branes incorporated into the gravity dual

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.