The 4-D Layer Phase as a Gauge Field Localization: Extensive Study of the 5-D Anisotropic U(1) Gauge Model on the Lattice

TL;DR

This paper investigates a 5D lattice Abelian gauge model with anisotropic couplings, confirming a Layer phase where gauge fields are localized in 4D, and analyzes the nature of phase transitions with improved lattice data.

Contribution

It provides extensive numerical evidence for the Layer phase in a 5D gauge model and clarifies the order and critical properties of phase transitions involved.

Findings

Confirmation of the Layer phase with Coulomb-like 4D forces and confining fifth dimension.

Identification of a weak first order transition separating the Layer phase from the strongly coupled phase.

Evidence of a second order transition between the Layer phase and the 5D Coulomb phase, with estimated critical exponents.

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.