Two-point function of a d=2 quantum critical metal in the limit kF→∞ , Nf→0 with NfkF fixed

We show that the fermionic and bosonic spectrum of $d=2$ fermions at finite density coupled to a critical boson can be determined nonperturbatively in the combined limit ${k}_F\ensuremath{\rightarrow}\ensuremath{\infty},\phantom{\rule{0.16em}{0ex}}{N}_f\ensuremath{\rightarrow}0$ with ${N}_f{k}_F$ fixed. In this double scaling limit, the boson two-point function is corrected but only at one loop. This double scaling limit therefore incorporates the leading effect of Landau damping. The fermion two-point function is determined analytically in real space and numerically in (Euclidean) momentum space. The resulting spectrum is discontinuously connected to the quenched ${N}_f\ensuremath{\rightarrow}0$ result. For $\ensuremath{\omega}\ensuremath{\rightarrow}0$ with $k$ fixed the spectrum exhibits the distinct non-Fermi-liquid behavior previously surmised from the RPA approximation. However, the exact answer obtained here shows that the RPA result does not fully capture the IR of the theory.