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Vanishing short multiplets in rank one 4d/5d SCFTs. (English) Zbl 07690775

Summary: 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.

MSC:

81-XX Quantum theory
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