Deconstructing {\" U}nsal-Yaffe Reconfinement

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.