A hidden classical symmetry of QCD
Institute of Physics, University of Graz, A-8010 Graz, Austria
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Published online: 5 December 2017
The classical part of the QCD partition function (the integrand) has, ignoring irrelevant exact zero modes of the Dirac operator, a local SU(2NF) ⊃ SU(NF)L × SU(NF)R × 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(2NF) symmetry in correlators and spectra. This naturally explains observation on the lattice of a large degeneracy of hadrons, that is higher than the SU(NF)L × SU(NF)R × U(1)A chiral symmetry, upon elimination by hands of the lowestlying modes of the Dirac operator. We also discuss an implication of this symmetry for the high temperature QCD.
© The Authors, published by EDP Sciences, 2017
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