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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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Cited by 1 Pith paper
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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.
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