# Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature

## TL;DR

This study investigates how low Dirac eigenmodes in 2+1D SU(3) pure gauge theory transition from delocalised to localised across the deconfinement temperature, revealing a BKT-type Anderson transition.

## Contribution

It provides the first numerical evidence of localisation transition in 2+1D SU(3) gauge theory and links it to deconfinement and chiral symmetry restoration.

## Key findings

- Localisation occurs at the deconfinement temperature.
- A BKT-type Anderson transition is observed in the Dirac spectrum.
- Localisation correlates with deconfinement and chiral symmetry restoration.

## Abstract

I study the localisation properties of low Dirac eigenmodes in 2+1 dimensional SU(3) pure gauge theory, both in the low-temperature, confined and chirally-broken phase and in the high-temperature, deconfined and chirally-restored phase, by means of numerical lattice simulations. While these modes are delocalised at low temperature, they become localised at high temperature, up to a critical point in the Dirac spectrum where a BKT-type Anderson transition takes place. All results point to localisation appearing at the deconfinement temperature, and support previous expectations about the close relation between deconfinement, chiral symmetry breaking, and localisation.