Breakdown of large-N quenched reduction in SU(N) lattice gauge theories

TL;DR

This paper investigates the breakdown of large-N reduction in SU(N) lattice gauge theories, showing through theoretical arguments and simulations that the quenched approximation fails due to dynamically generated correlations, challenging the validity of the reduction.

Contribution

The study provides the first comprehensive analysis combining weak-coupling arguments and Monte Carlo simulations to demonstrate the failure of large-N reduction in the quenched Eguchi-Kawai model.

Findings

Large-N equivalence likely breaks down in the QEK model.

Dynamically generated correlations cause reduction failure.

Monte Carlo simulations confirm the discrepancy in transition couplings.

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 find that the assumptions needed for the proofs of equivalence do not automatically follow from the quenching prescription. We use weak-coupling arguments to show that large-N equivalence is in fact likely to break down in the QEK model, and that this is due to dynamically generated correlations between different Euclidean components of the gauge fields. We then use Monte-Carlo simulations at intermediate couplings with 20 <= N <= 200 to provide strong evidence for the presence of these correlations and for the consequent breakdown of reduction. This evidence includes a large discrepancy between the transition coupling of the "bulk" transition in lattice gauge theories and the coupling at which the QEK model goes through a strongly first-order transition. To accurately measure this discrepancy we adapt the recently introduced Wang-Landau algorithm to gauge theories.