  Significant effort has been devoted to the study of "non-Fermi liquid" (NFL)
metals: gapless conducting systems that lack a quasiparticle description. One
class of NFL metals involves a finite density of fermions interacting with soft
order parameter fluctuations near a quantum critical point. The problem has
been extensively studied in a large N limit (N corresponding to the number of
fermion flavors) where universal behavior can be obtained by solving a set of
coupled saddle-point equations. However a remarkable study by S.-S.~Lee
revealed the breakdown of such approximations in two spatial dimensions. We
show that an alternate approach, in which the fermions belong to the
fundamental representation of a global SU(N) flavor symmetry, while the order
parameter fields transform under the adjoint representation (a "matrix large N"
theory), yields a tractable large N limit. At low energies, the system consists
of an overdamped boson with dynamical exponent $z=3$ coupled to a non-Fermi
liquid with self energy $\Sigma(\omega) \sim \omega^{2/3}$, consistent with
previous studies.
