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

Abstract

We study the short multiplet spectrum in 4d N = 2 superconformal theories of low rank using the full superconformal indices and the selection rules from the super conformal 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.