Vanishing short multiplets in rank one 4d/5d SCFTs

Abstract

We study the short multiplet spectrum in 4d $\mathcal{N}=2$ superconformal theories of low rank using the full superconformal indices and the selection rules from the superconformal representation theory. We find a universal expression for the leading terms for the superconformal index of rank one $H_0,H_1,H_2,D_4,E_6,E_7$ theories. From this result, we argue that certain short multiplets appear in the operator product expansions involving stress-tensor, conserved current, and Coulomb branch operator vanish. We also apply the same procedure to 5d superconformal theories and find that $E_1$ theory has vanishing short multiplets analogous to that of the $H_1$ theory.

arXiv comment20 pages, v2: minor corrections, reference added. to appear in JHEP

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