  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.
