Nonperturbative volume reduction of large-NQCD with adjoint fermions

Abstract

We use nonperturbative lattice techniques to study the volume-reduced ``Eguchi-Kawai'' version of four-dimensional large-$N$ QCD with a single adjoint Dirac fermion. We explore the phase diagram of this single-site theory in the space of quark mass and gauge coupling using Wilson fermions for a number of colors in the range $8\ensuremath{\le}N\ensuremath{\le}15$. Our evidence suggests that these values of $N$ are large enough to determine the nature of the phase diagram for $N\ensuremath{\rightarrow}\ensuremath{\infty}$. We identify the region in the parameter space where the $({Z}_{N}{)}^{4}$ center symmetry is intact. According to previous theoretical work using the orbifolding paradigm, and assuming that translation invariance is not spontaneously broken in the infinite-volume theory, in this region volume reduction holds: the single-site and infinite-volume theories become equivalent when $N\ensuremath{\rightarrow}\ensuremath{\infty}$. We find strong evidence that this region includes both light and heavy quarks (with masses that are at the cutoff scale), and our results are consistent with this region extending toward the continuum limit. We also compare the action density and the eigenvalue density of the overlap Dirac operator in the fundamental representation with those obtained in large-$N$ pure-gauge theory.