Phase structure of twisted Eguchi-Kawai model

TL;DR

This paper investigates the phase structure of the four-dimensional twisted Eguchi-Kawai model through numerical simulations, revealing that the continuum limit cannot be achieved due to symmetry breaking.

Contribution

It provides a detailed analysis of the symmetry breaking point in the model, highlighting limitations in taking the continuum limit.

Findings

Z_N^4 symmetry breaks spontaneously in the intermediate coupling region

Continuum limit of the model cannot be taken due to symmetry breaking

Numerical simulations clarify the phase transition behavior

Abstract

We study the phase structure of the four-dimensional twisted Eguchi-Kawai model using numerical simulations. This model is an effective tool for studying SU(N) gauge theory in the large-N limit and provides a nonperturbative formulation of the gauge theory on noncommutative spaces. Recently it was found that its Z_N^4 symmetry, which is crucial for the validity of this model, can break spontaneously in the intermediate coupling region. We investigate in detail the symmetry breaking point from the weak coupling side. Our simulation results show that the continuum limit of this model cannot be taken.