Perturbative non-Fermi liquids from bosonization

We develop a theory of a perturbative non-Fermi liquid fixed point but coupling a Fermi liquid in the "postmodern" formalism developed in [Delacretaz et al, PRR 2022] to a critical boson. This theory avails itself to a straightforward power counting analysis to characterize scaling dimensions of various operators without the need for the heuristics of patch decomposition. We report progress on the calculation of beta functions of various couplings and anomalous dimensions of operators at the fixed point.