Phase structure of pure SU(3) lattice gauge theory in 5 dimensions

Abstract

We investigate the nonperturbative phase structure of five-dimensional SU(3) pure Yang-Mills theory on the lattice. We perform numerical simulations using the Wilson plaquette gauge action on an anisotropic lattice with a four-dimensional lattice spacing (a 4 ) and with an independent value in the fifth dimension (a 5 ). We investigate both cases of a 4 > a 5 and a 4 < a 5 . The Polyakov loops in the fourth and the fifth directions are observed, and we find that there are four possible phases for the anisotropic five-dimensional quenched QCD theory on the lattice. We determine the critical values of the lattice bare coupling and the anisotropy parameter for each phase transition. Furthermore, we find that the two center domains where the Polyakov loop have locally different charges of the center symmetry appears in single configuration in the specific region of the lattice parameters.

Lifshitz-type SU(N) lattice gauge theory in five dimensions

“…2. There is a sharp drop at β ∼ 4.5, which is a known bulk transition from a confining phase at small β to a deconfined Coulomb phase at large β [15]. This is consistent with perturbative non-renormalizability of the Yang-Mills theory in five dimensions.…”

RG flows in Non-Perturbative Gauge-Higgs Unification II. Effective action for the Higgs phase near the quantum phase transition

“…Another way of seeing the above argument is that we want the fields and currents of S b−h to be localized at the lattice boundary. This happens when the anisotropy is small, [24], which is true when a 5 > a 4 . So since here we consider the a 4 → 0 limit then a 5 cannot approach zero but it can take any finite value without losing generality.…”

Symmetry breaking caused by large ℛ-charge

“…Field contents We consider SU(3) gauge theories which have been investigated in the context of the symmetry breaking via the Wilson line phase recently in [17,21] with the lattice gauge theory. Our model is constructed by…”

“…One naive way is to use the lattice gauge theory. The mechanism have been studied already by lattice gauge theories [16,17,18,19,20,21]. For example, in [17,18], they studied the SU(3) gauge symmetry in the 3+1 dimensional flat spacetime.…”