On the nature of an emergent symmetry in QCD

TL;DR

This paper investigates the emergent symmetry observed in lattice QCD calculations when low-lying Dirac eigenmodes are removed, concluding that the symmetry is larger than SU(4) and likely not continuous.

Contribution

It demonstrates that the observed symmetry pattern cannot be explained by any continuous symmetry generated by local operators, challenging previous assumptions about emergent symmetries in QCD.

Findings

Correlation functions in the SU(4) 15-plet and singlet coincide when low modes are removed.

No continuous symmetry generated by local operators accounts for the full pattern of identical correlation functions.

The apparent symmetry may be accidental rather than a fundamental emergent symmetry.

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.