  We initiate the study of correlation functions of non-Abelian spin-1
conserved current in three dimensional conformal field theories using numerical
conformal bootstrap. We discuss the general framework and apply it to the
particular cases of $SU(N)$ and $O(N)$ global symmetry. In both cases we obtain
general bounds on operator dimensions. In the large-$N$ limit our bounds show
features in correspondence of the expected position of fermionic QED$_3$ in
three dimensions, as well as other interesting theories. By imposing gaps
inspired by the spectrum of QED$_3$ at large-$N$, we manage to restrict the
plane of certain operator dimensions to a small island, where QED$_3$ must
live.
