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

Abstract

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 $\mathcal{N}=7$ superconformal theory is in fact enhanced to $\mathcal{N}=8$. 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.

7 pages

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Cited by in corpus (6)

• Studying superconformal symmetry enhancement through indices
• Reflection groups and 3d $\mathcal{N}\ge$ 6 SCFTs
• Relations between supersymmetric structures in UV and IR for $\mathcal{N}=4$ bad theories
• Duality between N=5 and N=6 Chern-Simons matter theory
• Lectures on 4d N=1 dynamics and related topics
• Factorization of the 3d superconformal index with an adjoint matter