Large $N$ reduction with the Twisted Eguchi-Kawai model

TL;DR

This paper investigates the $Z_N$ symmetry breaking in the Twisted Eguchi-Kawai model and proposes modifications to prevent it, enabling accurate large $N$ limit calculations of string tension.

Contribution

It identifies the cause of symmetry breaking in TEK and introduces simple modifications to preserve symmetry, improving large $N$ extrapolations.

Findings

No evidence of $Z_N$ symmetry breaking with modifications

Accurate large $N$ string tension values obtained

Results align with traditional extrapolation methods

Abstract

We examine the breaking of $Z_N$ symmetry recently reported for the Twisted Eguchi-Kawai model (TEK). We analyse the origin of this behaviour and propose simple modifications of twist and lattice action that could avoid the problem. Our results show no sign of symmetry breaking and allow us to obtain values of the large $N$ infinite volume string tension in agreement with extrapolations from results based upon straightforward methods.