Toward precision Fermi liquid theory in flatland

: The ultra-cold and weakly-coupled Fermi gas in two spatial dimensions is studied in an eﬀective ﬁeld theory framework. Universal corrections to the energy density are computed to three orders in the interaction strength with special consideration given to the scale ambiguity associated with the non-trivial renormalization of the singular contact interactions. The isotropic superﬂuid gap is obtained to next-to-leading order, and nonuniversal contributions to the energy density due to eﬀective range eﬀects, p-wave interactions and three-body forces are computed. Results are compared with precise Monte Carlo simulations of the energy density and the contact in the weakly-coupled attractive and repulsive Fermi liquid regimes. In addition, the known all-orders sum of ladder and ring diagrams is compared with Monte Carlo simulations at weak coupling and beyond.