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

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.