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.
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