U(1) axial symmetry and Dirac spectra in QCD at high temperature

TL;DR

This paper provides exact theoretical results on the behavior of U(1)$_A$ symmetry in high-temperature QCD, emphasizing topology, finite-volume effects, and spectral properties, with implications for lattice simulations.

Contribution

It introduces a reliable method to measure anomaly strength in lattice QCD, derives new spectral sum rules, and offers an alternative proof of U(1)$_A$ symmetry restoration at high temperature.

Findings

Derived exact results on U(1)$_A$ symmetry in high-temperature QCD.

Presented a new method to measure anomaly strength in lattice simulations.

Established spectral sum rules and a Banks-Casher-type relation.

Abstract

We derive some exact results concerning the anomalous U(1)$_A$ symmetry in the chirally symmetric phase of QCD at high temperature. We discuss the importance of topology and finite-volume effects on the U(1)$_A$ symmetry violation characterized by the difference of chiral susceptibilities. In particular, we present a reliable method to measure the anomaly strength in lattice simulations with fixed topology. We also derive new spectral sum rules and a novel Banks-Casher-type relation. Through our spectral analysis we arrive at a simple alternative proof of the Aoki-Fukaya-Taniguchi "theorem" on the effective restoration of the U(1)$_A$ symmetry at high temperature.