QED's in $2{+}1$ dimensions: complex fixed points and dualities

Abstract: We consider Quantum Electrodynamics with an even number $N_f$ of bosonic or fermionic flavors, allowing for interactions respecting at least $U(N_f/2)^2$ global symmetry. Both in the bosonic and in the fermionic case, we find four interacting fixed points: two with $U(N_f/2)^2$ symmetry, two with $U(N_f)$ symmetry. Large $N_f$ arguments suggest that, lowering $N_f$, all these fixed points merge pairwise and become complex CFT's. In the bosonic QED's the merging happens around $N_f\sim 9{-}11$ and does not break the global symmetry. In the fermionic QED's the merging happens around $N_f\sim3{-}7$ and breaks $U(N_f)$ to $U(N_f/2)^2$. When $N_f=2$, we show that all four bosonic fixed points are one-to-one dual to the fermionic fixed points. The merging pattern suggested at large $N_f$ is consistent with the four $N_f=2$ boson $\lra$ fermion dualities, providing support to the validity of the scenario.