Realization of Center Symmetry in Two Adjoint Flavor Large-N Yang-Mills
Simon Catterall, Richard Galvez, Mithat Unsal
TL;DR
This work examines center symmetry and large-$N$ volume independence (Eguchi-Kawai reduction) for $SU(N)$ gauge theories with two adjoint Wilson fermions on a $2^4$ lattice. A weak-coupling one-loop analysis shows that for massless fermions the center-symmetric phase is independent of the volume reduction parameter $\Gamma$, and simulations extend the check to finite coupling and nonzero mass. Numerically, the quenched theory exhibits a transition at $\lambda_c \approx 3.0$ between broken and unbroken center symmetry in the large-$N$ limit, while dynamical adjoint fermions suppress the Polyakov loop and restore center symmetry at large $N$ over a range of masses near the critical line. These results support using small-volume, large-$N$ simulations to access infinite-volume observables and to inform the conformal window for adjoint theories, including implications for the minimal walking theory.
Abstract
We report on the results of numerical simulations of $SU(N)$ lattice Yang Mills with two flavors of (light) Wilson fermion in the adjoint representation. We analytically and numerically address the question of center symmetry realization on lattices with $Γ$ sites in each direction in the large-$N$ limit. We show, by a weak coupling calculation that, for massless fermions, center symmetry realization is independent of $Γ$, and is unbroken. Then, we extend our result by conducting simulations at non zero mass and finite gauge coupling. Our results indicate that center symmetry is intact for a range of fermion mass in the vicinity of the critical line on lattices of volume $2^4$. This observation makes it possible to compute infinite volume physical observables using small volume simulations in the limit $N\to\infty$, with possible applications to the determination of the conformal window in gauge theories with adjoint fermions.