Two-loop fermion self-energy and propagator in reduced QED${}_{3,2}$

We compute the two-loop fermion self-energy in massless reduced quantum electrodynamics (RQED) for an arbitrary gauge in the case where the photon field is three-dimensional and the fermion field two-dimensional: super-renormalizable RQED${}_{3,2}$ with $N_F$ fermions. We find that the theory is infrared finite at two-loop and that finite corrections to the fermion propagator have a remarkably simple form.