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

TL;DR

This study uses large lattice Monte Carlo simulations to investigate the phase structure of five-dimensional anisotropic SU(2) Yang-Mills theory, challenging previous claims about a transition to a layered phase and the viability of dimensional reduction.

Contribution

It provides evidence that the transition remains first order at larger lattices, questioning the existence of a layered phase for dimensional reduction.

Findings

First order phase transition at $eta_4=2.60$ confirmed

Large lattices are necessary to determine transition order

Layered phase scenario is unlikely based on results

Abstract

We extend to large lattices the work of a previous investigation of the phase diagram of the anisotropic five-dimensional SU(2) Yang-Mills model using Monte Carlo simulations in the regime where the lattice spacing in the fifth dimension is larger than in the other four dimensions. We find a first order phase transition between the confining and deconfining phase at the anisotropic parameter point $\beta_4=2.60$ which was previously claimed to be the critical point at which the order of the transition changes from first to second. We conclude that large lattices are required to establish the first order nature of this line of transitions and consequently that the scenario of dimensional reduction of the five-dimensional theory to a continuum four-dimensional theory via the existence of the so-called "layer phase" is unpromising.