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

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.

28 pages, 2 figures; v2: Section 2 was substantially rewritten and Section 4 was omitted. published version

References in corpus (4)

• Meson screening masses from lattice QCD with two light and the strange quark
• Chiral Lagrangian and spectral sum rules for dense two-color QCD
• Dense QCD in a Finite Volume
• Chiral symmetry breaking with no bilinear condensate revisited

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