Exploration of the phase diagram of 5D anisotropic SU(2) gauge theory

Abstract

In this paper we attempt a non-perturbative study of the five dimensional, anisotropic SU(2) gauge theory on the lattice using Monte-Carlo techniques. Our goal is the exploration of the phase diagram, define the various phases and the critical boundary lines. Three phases appear, two of them are continuations of the Strong and the Weak coupling phases of pure 4d SU(2) to non-zero coupling β ′ in the fifth transverse direction and they are separated by a crossover transition, while the third phase is a 5d Coulombic phase. We provide evidence that the phase transition between the 5D Coulomb phase and the Weak coupling phase is a second order phase transition. Assuming that this result is not altered when increasing the lattice volume we give a first estimate of the associated critical exponents. This opens the possibility for a continuum effective five dimensional field theory. *

The transition to a layered phase in the anisotropic five-dimensional SU(2) Yang–Mills theory

“…2). The critical β 5 point was found to be β 5 = 0.8437(5) which agrees within error with the value found in [20]. For the investigation of the phase transition on the larger lattices we focused on the critical region which was estimated to be between β 5 = 0.843 and β 5 = 0.8445, based on the critical value found for the 16 5 lattice.…”

“…The existence of the layer phase was investigated by mean-field approximation on an anisotropic lattice with periodic boundary conditions [18,19] and it was shown that the planes transverse to the extra dimension were decoupled from each other. An investigation of the existence of this layer phase using Monte Carlo techniques was attempted by Farakos et al [20]. They claim that the transition between the five-dimensional Coulombic (deconfined) phase and the strong-coupling (confined) phase changes its order from first to second, implying that in the fifth dimension the layer phase exists.…”

“…The motivation for studying this model further came mostly from results in [9], which indicate that the lattice volumes used in the previous Monte Carlo simulations [20], were too small to show the correct order of the phase transition. In this letter we extend this investigation to larger volumes.…”

Five-dimensional Gauge-Higgs Unification: a Standard Model-like Spectrum

“…However, their reconciliation was confirmed by the discovery of a global symmetry in [24]; it is the spontaneous breaking of this global symmetry which leads to the BEH mechanism in the context of non-perturbative GHU models [25]. Other previous explorations of this theory have focused on the case of a toroidal geometry which is known to posses confined and de-confined phases separated by a first-order phase transition [26][27][28][29][30]; second-order transitions due to compactification were studied in [27,31,32], and the scalar spectrum was measured in [33].…”

Dimensional reduction and confinement from five dimensions

“…So far we located a line of first order bulk phase transitions. It has been recently claimed in [8] that this phase transition could be of second order for parameters that are outside the range we investigate in this talk (see Fig. 4).…”