# The localization transition in SU(3) gauge theory

## TL;DR

This paper investigates the Anderson-like localization transition in the Dirac spectrum of quenched QCD, revealing that the disappearance of localized modes coincides with the deconfining transition temperature.

## Contribution

It provides the first detailed analysis of the temperature dependence of the mobility edge in quenched QCD and its relation to the deconfining transition.

## Key findings

- The mobility edge vanishes at the deconfining temperature.
- Localized modes are only weakly related to topological charge near zero modes.
- The fraction of localized modes decreases rapidly with increasing temperature.

## Abstract

We study the Anderson-like localization transition in the spectrum of the Dirac operator of quenched QCD. Above the deconfining transition we determine the temperature dependence of the mobility edge separating localized and delocalized eigenmodes in the spectrum. We show that the temperature where the mobility edge vanishes and localized modes disappear from the spectrum, coincides with the critical temperature of the deconfining transition. We also identify topological charge related close to zero modes in the Dirac spectrum and show that they account for only a small fraction of localized modes, a fraction that is rapidly falling as the temperature increases.