Localization at the quenched SU(3) phase transition

TL;DR

This paper investigates how the localization of low Dirac eigenmodes in quenched SU(3) gauge theory changes at the deconfinement transition, revealing a discontinuity in the mobility edge in the real Polyakov loop sector.

Contribution

It provides a detailed analysis of the abrupt change in localization properties of Dirac modes at the critical temperature in quenched SU(3), highlighting sector-dependent behavior.

Findings

Localization changes abruptly at the critical temperature in the real Polyakov loop sector.

Mobility edge exhibits a discontinuity at T_c in the real sector.

In the complex sector, low Dirac modes remain delocalized at T_c.

Abstract

It is known that the deconfining transition of QCD is accompanied by the appearance of localized eigenmodes at the low end of the Dirac spectrum. In the quenched case localization appears exactly at the critical temperature of deconfinement. In the present work, using quenched simulations exactly at the critical temperature, we show that the localization properties of low Dirac modes change abruptly between the confined and deconfined phase. This means that in the real Polyakov loop sector, the mobility edge has a discontinuity at the critical temperature. In contrast, in the complex sector, there is no such discontinuity at $T_c$, even the lowest Dirac modes remain delocalized at the critical temperature in the deconfined phase.