Deconstructing finite temperature pure gauge theory

TL;DR

This paper explores a deconstructed finite temperature pure gauge theory, revealing how adding gauge-invariant Polyakov loop terms significantly alters the Hilbert space structure and has implications for large N reduction.

Contribution

It introduces a framework for analyzing deformed finite temperature gauge theories, showing how deformations change the Hilbert space and impact large N reduction.

Findings

Deformation causes a shift from a gauge singlet Hilbert space to one including all local SU(N)/Z(N) states.

Adding Polyakov loop terms affects the ultraviolet behavior, making it effectively one dimension lower.

Implications for large N reduction are discussed in the context of these deformations.

Abstract

A deconstructed finite temperature gauge theory has the Euclidean time direction kept discrete and finite. The ultraviolet behavior is that of one dimension less than at zero temperature. One can add to the action a gauge invariant term dependent on Polyakov loops, without worrying about nonlocality. The deformation of {\" U}nsal and Yaffe is best analyzed in this framework. It is shown that turning it on causes a dramatic change in the Hilbert space on which the transfer matrix in the temperature direction acts. The undeformed Hilbert space is everywhere a gauge singlet while the deformed one includes all states transforming locally, anywhere, under any SU(N)/Z(N) irreducible representation. Implications of this in the context of large N reduction are discussed.