Breakdown of large-N reduction in the quenched Eguchi-Kawai model

TL;DR

This paper investigates the failure of large-N reduction in the quenched Eguchi-Kawai model, showing that the equivalence breaks down in the weak-coupling regime due to dynamically generated correlations, based on analytic and simulation evidence.

Contribution

The paper provides a detailed analysis demonstrating the breakdown of large-N reduction in the QEK model in the continuum limit, with intuitive explanations and supporting evidence.

Findings

Large-N equivalence does not hold in the weak-coupling regime.

Breakdown caused by dynamically generated correlations between gauge field components.

Evidence from analytic arguments and Monte Carlo simulations with N up to 200.

Abstract

We study the validity of the large-N equivalence between four-dimensional SU(N) lattice gauge theory and its momentum quenched version -- the Quenched Eguchi-Kawai (QEK) model. We have found strong evidence that this equivalence does not hold in the weak-coupling regime (and thus in the continuum limit). This is based on weak-coupling analytic arguments and Monto-Carlo simulations at intermediate couplings with 20 <= N <= 200. Since detailed expositions of our arguments, methods and results have already appeared in Phys. Rev. D78:034507 (2008) and Phys. Rev. D78:074503 (2008), we attempt here to give a more intuitive explanation of our results. The breakdown of reduction that we find is due to a dynamically generated correlation between different Euclidean components of the gauge fields.