| Summary: | Abstract 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.
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