4-dimensional layer phase as a gauge field localization: Extensive study of the 5-dimensional anisotropic U(1) gauge model on the lattice

Abstract

We study a 4+1 dimensional pure Abelian Gauge model on the lattice with two anisotropic couplings independent of each other and of the coordinates. A first exploration of the phase diagram using mean field approximation and monte carlo techniques has demonstrated the existence of a new phase, the so called Layer phase, in which the forces in the 4-D subspace are Coulomb-like while in the transverse direction (fifth dimension) the force is confining. This allows the possibility of a gauge field localization scheme. In this work the use of bigger lattice volumes and higher statistics confirms the existence of the Layer phase and furthermore clarifies the issue of the phase transitions' order. We show that the Layer phase is separated from the strongly coupled phase by a weak first order phase transition. Also we provide evidence that the Layer phase is separated by the five-dimensional Coulomb phase with a second order phase transition and we give a first estimation of the critical exponents. *

Lattice gauge theory approach to spontaneous symmetry breaking from an extra dimension

“…This anisotropy could give rise to a new, so-called layered, phase where the static force is of Coulomb type in the four-dimensional slices and confining along the extra dimension, thus providing a localization mechanism. Some evidence for the existence of the layered phase in Abelian gauge theory was recently given in [25]. Another similar idea was due to [26] where it is assumed that the system has a phase where the bulk is in a confined while the boundary (defined by a domain wall) is in a deconfined phase, which forces the boundary gauge fields to remain localized.…”

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

“…We assume that the pseudo-critical value of the transverse gauge coupling scales with the lattice length according to the expression [9]: or equivalently:…”

“…Note that the transition line between the Strong coupling (β < 1) phase and the Layer phase (β > 1, β ′ < 0.4) is weakly first order. The phase transition between the Layer phase and the five-dimensional Coulomb phase, β ′ > 0.4, is probably of second order [9], while the transition from the Strong coupling to 5D Coulomb phase is a strong first order phase transition.…”

Finite temperature and confinement along the extra dimensions studied on a five-dimensional U(1) lattice gauge model

“…(ii) For the transition between the 5D Coulomb phase and the layer phase, h S ðÞ retains a value close to 1 for all values of 0 , since the four-dimensional layers experience already a 4D Coulomb-like phase, while h 5 ð 0 Þ vanishes for the layer phase; as the system crosses the critical point and enters the Coulomb phase it grows towards 1 as 0 increases further [4,15].…”

“…Since then many numerical investigations of the model have been made [15,16]. As we have already noted in the Introduction, the interest in this comes from the fact that the anisotropy of the model produces a new phase, the so-called layer phase, which can serve as a mechanism for gauge field localization on a brane.…”