On the nature of an emergent symmetry in QCD

Abstract

Remarkable symmetry properties appear to arise in lattice calculations of correlation functions in which the lowest-lying eigenmodes of the Dirac operator in quark propagators are removed by hand. The Banks-Casher relation ties the chiral condensate to the density of low lying modes; thus, it is plausible that removal of such modes could lead to a regime where spontaneous chiral symmetry breaking does not occur. Surprising, a pattern of identical correlation functions was observed that is larger than can be explained by a restoration of chiral symmetry. This suggests that a larger symmetry---one that is not present in the QCD lagrangian---emerges when these modes are removed. Previously it was argued that this emergent symmetry was SU(4). However, when the low-lying modes are removed, the correlation functions of sources in the SU(4) 15-plet of spin-1 mesons appear to coincide with the correlation function of the SU(4) singlet. A natural explanation for this is an emergent symmetry larger than SU(4). In this work, it is shown that there exists no continuous symmetry whose generators in the field theory are spatial integrals of local operators that can account for the full pattern of identical correlation functions unless the apparent coincidence of the singlet channel with the 15-plet is accidental.

References added; A few clarifying comments added

References in corpus (7)

• Symmetries of hadrons after unbreaking the chiral symmetry
• Isoscalar mesons upon unbreaking of chiral symmetry
• SU(4) symmetry of the dynamical QCD string and genesis of hadron spectra
• Overlap Quark Propagator in Coulomb Gauge QCD and the Interrelation of Confinement and Chiral Symmetry Breaking
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Cited by in corpus (5)

• Chiral spin symmetry and hot/dense QCD
• A hidden classical symmetry of QCD
• Dynamically Emergent Flavor in a Confining Theory with Unbroken Chiral Symmetry
• $SU(2N_F)$ symmetry of confinement in QCD and its observation at high temperature
• Chiral symmetry restoration in static-light mesons: chiral restoration theorem, the quark running mass m(k) and first chiral restoration signals in the lattice QCD spectra