Wilsonian and Large N Approaches to Non-Fermi Liquids

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We study the problem of metals near a quantum critical point using a local Wilsonian effective field theory of Fermi surface fermions coupled to massless boson (i.e. order parameter) fields, in particular in a large N limit where the boson is matrix-valued. We focus on regions of parameter space where the boson dresses the fermions into a non-Fermi liquid while the bosons are approximately controlled by the Wilson-Fisher fixed point.