  Anomalous metals are observed in numerous experiments on disordered
two-dimensional systems proximate to superconductivity. A characteristic
feature of an anomalous metal is that its low temperature conductivity has a
weakly temperature dependent value, significantly higher than that of a
disordered Fermi liquid. We propose a dynamical mean-field model of an
anomalous metal: interacting electrons similar in structure to that of the
well-studied universal Hamiltonian of mesoscopic metallic grains, but with
independent random interactions between pairs of sites, involving Cooper pair
hopping and spin exchange. We find evidence for critical anomalous phases or
points between a superconducting phase and a disordered Fermi liquid phase in
this model. Our results are obtained by a renormalization group analysis in a
weak coupling limit, and a complementary solution at large $M$ when the spin
symmetry is generalized to USp($M$). The large $M$ limit describes the
anomalous metal by fractionalization of the electron into spinons, holons, and
doublons, with these partons forming critical non-Fermi liquids in the
Sachdev-Ye-Kitaev class. We compute the low temperature conductivity in the
large $M$ limit, and find temperature-independent values moderately enhanced
from that in the disordered metal.
