A note on $\mathcal{N}\ge 6$ Superconformal Quantum Field Theories in three dimensions

Based on the structure of the three-dimensional superconformal algebra we show that every irreducible $\mathcal{N}=6$ three-dimensional superconformal theory containes exactly one conserved U(1)-symmetry current in the stress tensor supermultiplet and that superconformal symmetry of every ${\mathcal N}=7$superconformaltheoryisinfactenhancedto${\mathcal N}=8$. Moreover, an irreducible $\mathcal{N}=8$ superconformal theory does not have any global symmetries. The first observation explains why all known examples of ${\mathcal N}=6$ superconformal theories have a global abelian symmetry.