Deconstructing {\" U}nsal-Yaffe Reconfinement

TL;DR

This paper investigates the properties of the UY reconfined phase on a lattice, revealing differences in state representations and raising concerns about large N reduction methods.

Contribution

It analyzes the representation structure of the UY reconfined phase and discusses implications for large N Eguchi-Kawai reduction.

Findings

Thermal trace includes all $SU(N)/Z(N)$ representations in UY phase.

On finite lattices, the Hilbert space becomes orthogonal to the deformed one as N increases.

Concerns are raised about the validity of large N reduction in this context.

Abstract

In the UY reconfined phase on a lattice the thermal trace is over states transforming in all $SU(N)/Z(N)$ irreducible representations as opposed to only over $SU(N)$ singlets in the standard formulation. As $N\to\infty$, on a finite lattice, the usual Hilbert space becomes orthogonal to the deformed one. Concerns about the extended UY proposal for large $N$ Eguchi-Kawai reduction are raised.