Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2011-06-27
Physics
High Energy Physics
High Energy Physics - Lattice
58 pages, 28 figures
Scientific paper
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, a*m, 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 Phys. Rev. D80: 065031), 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, while we cannot rule out that it shrinks to zero at infinite N, the bulk of the evidence suggests that it remains of finite width. 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 infinite N, apply also for the large volume theory, which is minimal walking technicolor with N=infinity. We find a first-order transition as a function of a*m for all values of b, which we argue favors that the theory is confining in the infrared. Our results for the average plaquette prefer a linear dependence on 1/N, rather than the expected quadratic form, and we discuss a possible explanation for this. 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.
Bringoltz Barak
Koren Mateusz
Sharpe Stephen R.
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