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

Abstract

Abstract We study the short multiplet spectrum in 4d N $$ \mathcal{N} $$ = 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.

Keywords

• Extended Supersymmetry
• Field Theories in Higher Dimensions
• Scale and Conformal Symmetries