Easy-plane QED$_3$'s in the large $N_f$ limit

We consider Quantum Electrodynamics in $2{+}1$ dimensions with $N_f$ fermionic or bosonic flavors, allowing for interactions that respect the global symmetry $U(N_f/2)^2$. There are four bosonic and four fermionic fixed points, which we analyze using the large $N_f$ expansion. We systematically compute, at order $O(1/N_f)$, the scaling dimensions of quadratic and quartic mesonic operators. We also consider Quantum Electrodynamics with minimal supersymmetry. In this case the large $N_f$ scaling dimensions, extrapolated at $N_f{=}2$, agree quite well with the scaling dimensions of a dual supersymmetric Gross-Neveu-Yukawa model. This provides a quantitative check of the conjectured duality.