In high-temperature two-flavor lattice QCD, the axial U(1) and topological susceptibilities nearly vanish at small quark mass, consistent with axial U(1) symmetry restoration in the chiral limit.
U(1) axial symmetry and Dirac spectra in QCD at high temperature
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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.
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Axial U(1) symmetry, topology, and Dirac spectra at high temperature in $N_f=2$ lattice QCD
In high-temperature two-flavor lattice QCD, the axial U(1) and topological susceptibilities nearly vanish at small quark mass, consistent with axial U(1) symmetry restoration in the chiral limit.