Quenched divergences in the deconfined phase of SU(2) gauge theory

TL;DR

This paper investigates the behavior of small eigenvalues of the overlap Dirac operator in the deconfined phase of quenched SU(2) gauge theory, revealing a divergence of the chiral condensate with increasing volume.

Contribution

It provides a detailed analysis of the low-lying spectrum in quenched SU(2) gauge theory, highlighting the divergence of the chiral condensate in the deconfined phase.

Findings

Small eigenvalues concentrate near zero as volume increases

Chiral condensate appears to diverge in the infinite volume limit

Spectrum analysis suggests non-trivial topological effects in deconfined phase

Abstract

The spectrum of the overlap Dirac operator in the deconfined phase of quenched gauge theory is known to have three parts: exact zeros arising from topology, small nonzero eigenvalues that result in a non-zero chiral condensate, and the dense bulk of the spectrum, which is separated from the small eigenvalues by a gap. In this paper, we focus on the small nonzero eigenvalues in an SU(2) gauge field background at $\beta=2.4$ and $N_T=4$. This low-lying spectrum is computed on four different spatial lattices ($12^3$, $14^3$, $16^3$, and $18^3$). As the volume increases, the small eigenvalues become increasingly concentrated near zero in such a way as to strongly suggest that the infinite volume condensate diverges.