Abstract
We compute general expressions for two types of three-point functions of (semi-)short multiplets in four-dimensional \( \mathcal{N}=2 \) superconformal field theories. These (semi-)short multiplets are called “Schur multiplets” and play an important role in the study of associated chiral algebras. The first type of the three-point functions we compute involves two half-BPS Schur multiplets and an arbitrary Schur multiplet, while the second type involves one stress tensor multiplet and two arbitrary Schur multiplets. From these three-point functions, we read off the corresponding OPE selection rules for the Schur multiplets. Our results particularly imply that there are non-trivial selection rules on the quantum numbers of Schur operators in these multiplets. We also give a conjecture on the selection rules for general Schur multiplets.
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Kiyoshige, K., Nishinaka, T. OPE selection rules for Schur multiplets in 4D \( \mathcal{N}=2 \) superconformal field theories. J. High Energ. Phys. 2019, 60 (2019). https://doi.org/10.1007/JHEP04(2019)060
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DOI: https://doi.org/10.1007/JHEP04(2019)060