Year: 2012
Type: article
Abstract: We use lattice simulations to study the single-site version of $SU(N)$ lattice gauge theory with two flavors of Wilson-Dirac fermions in the adjoint representation, a theory whose large-volume correspondent is expected to be conformal or nearly conformal. Working with $N$ as large as 53, we map out the phase diagram in the plane of bare `t Hooft coupling, ${g}^{2}N$, and of the lattice quark mass, am, and look for the region where the ${Z}_{N}^{4}$ center symmetry of the theory is intact. In this region one expects the large-$N$ equivalence of the single-site and infinite volume theories to be valid. As for the ${N}_{f}=1$ case (see [B. Bringoltz and S. R. Sharpe, Phys. Rev. D 80, 065031 (2009)]), we find that the center-symmetric region is large and includes both light fermion masses and masses at the cutoff scale. We study the $N$-dependence of the width of this region and find strong evidence that it remains of finite width as $N\ensuremath{\rightarrow}\ensuremath{\infty}$. Simulating with couplings as small as ${g}^{2}N=0.005$, we find that the width shrinks slowly with decreasing ${g}^{2}N$, at a rate consistent with analytic arguments. Within the center-symmetric region our results for the phase structure, when extrapolated to $N=\ensuremath{\infty}$, apply also for the large-volume theory, which is minimal walking technicolor at $N=\ensuremath{\infty}$. We find a first-order transition as a function of am for all values of $b$, which we argue favors that the theory is confining in the infrared. Finally, we measure the eigenvalue densities of the Wilson-Dirac operator and its Hermitian version, and use large Wilson loops to study the utility of reduction for extracting physical observables.
Institutions: University of Washington, Jagiellonian University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: U.S. Department of Energy
OpenAlex ID: W2121533319