TL;DR
This paper reveals a hidden classical SU(2N_F) symmetry in the QCD partition function, which emerges when near-zero modes are truncated, explaining lattice observations of hadron degeneracy beyond known chiral symmetries.
Contribution
It identifies a hidden classical SU(2N_F) symmetry in QCD that becomes apparent through near-zero mode truncation, linking lattice results to fundamental symmetries.
Findings
Lattice truncation reveals a larger hadron degeneracy.
The hidden symmetry explains observed spectral degeneracies.
Implications for high-temperature QCD are discussed.
Abstract
The classical part of the QCD partition function (the integrand) has, ignoring irrelevant exact zero modes of the Dirac operator, a local SU(2N_F) \supset SU(N_F)_L \times SU(N_F)_R \times U(1)_A symmetry which is absent at the Lagrangian level. This symmetry is broken anomalously and spontaneously. Effects of spontaneous breaking of chiral symmetry are contained in the near-zero modes of the Dirac operator. If physics of anomaly is also encoded in the same near-zero modes, then their truncation on the lattice should recover a hidden classical SU(2N_F) symmetry in correlators and spectra. This naturally explains observation on the lattice of a large degeneracy of hadrons, that is higher than the SU(N_F)_L \times SU(N_F)_R \times U(1)_A chiral symmetry, upon elimination by hands of the lowest-lying modes of the Dirac operator. We also discuss an implication of this symmetry for the high…
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