Phase structure of twisted Eguchi-Kawai model

TL;DR

This paper investigates the phase structure of the twisted Eguchi-Kawai model using Monte Carlo simulations, revealing that the Z_N^4 symmetry breaks spontaneously and a continuum limit cannot be achieved.

Contribution

It provides a detailed analysis of the symmetry breaking in the model and clarifies the limitations for continuum limit realization.

Findings

Z_N^4 symmetry breaks spontaneously in the intermediate coupling region

Continuum limit cannot be taken in this model

Symmetry breaking point studied from the weak coupling side

Abstract

Twisted Eguchi-Kawai model is a useful tool for studying the large-N gauge theory. It can also provide a nonperturbative formulation of the gauge theory on noncommutative spaces. Recently it was found that the Z_N^4 symmetry in this model, which is crucial for the above applications, can break spontaneously in the intermediate coupling region. In this article, we study the phase structure of this model using the Monte-Carlo simulation. In particular, we elaborately investigate the symmetry breaking point from the weak coupling side. The simulation results show that we cannot take a continuum limit for this model.