# Localization and topology in high temperature QCD

## TL;DR

This paper investigates the relationship between localization of quark eigenmodes and the chiral crossover in high temperature QCD, analyzing gauge configurations and eigenmodes to understand the underlying mechanisms.

## Contribution

It provides an analysis of localized states in high temperature QCD and argues against calorons being the primary cause of localization.

## Key findings

- Localized states appear at the low end of the spectrum above the crossover temperature.
- Calorons are unlikely to be the main support for localized eigenmodes.
- Localization correlates with the chiral transition but is not driven by calorons.

## Abstract

At high temperature part of the spectrum of the quark Dirac operator is known to consist of localized states. This comes about because around the crossover temperature to the quark-gluon plasma localized states start to appear at the low end of the spectrum and as the system is further heated, states higher up in the spectrum also get localized. Since localization and the crossover to the chirally restored phase happen around the same temperature, the question of how the two phenomena are connected naturally arises. Here we speculate on the nature of possible gauge configurations that could support localized quark eigenmodes. In particular, by analyzing eigenmodes of the staggerd and overlap Dirac operator we show that the dilute gas of calorons in the high temperature phase is very unlikely to play a major role in localization.