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

TL;DR

The paper investigates the persistence of large-$N$ reduction in the Twisted Eguchi-Kawai model by analyzing the origin of $Z_N^4$ symmetry breaking at weak coupling and proposing modifications to the twist and lattice action. It combines weak-coupling perturbative analysis, fluxon considerations, and Monte Carlo simulations across (L,k) to identify symmetry-preserving regimes and extract infinite-volume observables. The authors show that a symmetric twist with $N=L^2$ and $n_{}= k L$ (with $k$ coprime to $L$) stabilizes the symmetry, with the critical coupling scaling roughly as $b_c(L,k) \sim L/k$, and they obtain string-tension estimates $\sigma \approx 0.56$–$0.58$ for $L=23$, $k=7$, in good agreement with large-$N$ extrapolations. This supports using TEK as a practical regulator for large-$N$ Yang–Mills observables and clarifies how to choose twist parameters to avoid symmetry breaking in the continuum reduction limit.

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.