Electrons Lost in Phase Space

Abstract

I review the formalism of patch bosonization of Fermi surfaces, with a focus on the problem of a two-dimensional metal at a quantum critical point. I argue that this formalism is fundamentally inapplicable to the problem, except in synthetic limits. One such limit is the small-$N$ limit, which was already discussed in early studies of the problem; a similar but slightly less unphysical large-$N$ limit is proposed. I show that it is at least formally possible to construct perturbative expansions around these synthetic limits. However, I argue that nonperturbative effects become important when $N\sim1$.