Realization of Center Symmetry in Two Adjoint Flavor Large-N Yang-Mills

TL;DR

This paper investigates the realization of center symmetry in large-N SU(N) lattice Yang-Mills theories with two adjoint fermion flavors, demonstrating that symmetry remains unbroken under various conditions, enabling small volume computations of physical observables.

Contribution

The study provides analytical and numerical evidence that center symmetry is preserved in large-N SU(N) theories with adjoint fermions across different lattice volumes and fermion masses.

Findings

Center symmetry remains unbroken for massless fermions.

Center symmetry is preserved for a range of non-zero fermion masses.

Small volume simulations can reliably compute infinite volume observables at large N.

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 $\Gamma$ 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 $\Gamma$, 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.