Non-Abelian currents bootstrap

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 QED₃ in three dimensions, as well as other interesting theories. By imposing gaps inspired by the spectrum of QED₃ at large-N, we manage to restrict the plane of certain operator dimensions to a small island, where QED₃ must live.