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arXiv · 1608.07269

A hidden classical symmetry of QCD

L. Ya. Glozman
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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 temperature QCD.

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L. Ya. Glozman. 2016-08-25. A hidden classical symmetry of QCD. https://doi.org/10.1051/epjconf%2F201716403002

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