The quenched Eguchi-Kawai model revisited

TL;DR

This paper revisits the quenched Eguchi-Kawai model, clarifying its original formulation and addressing previous claims of failure by demonstrating a formulation without annealed averages over permutations.

Contribution

It provides a detailed review of the original QEK model and offers a reformulation that avoids the issues identified in earlier critiques.

Findings

Original quenching logic leads to a formulation without annealed permutation averages

Clarifies the construction of the QEK model with greater detail

Addresses and refutes previous claims of model failure

Abstract

The motivation and construction of the original Quenched Eguchi-Kawai model are reviewed, providing much greater detail than in the first, 1982 QEK paper. A 2008 article announced that QEK fails as a reduced model because the average over permutations of eigenvalues stays annealed. It is shown here that the original quenching logic naturally leads to a formulation with no annealed average over permutations.