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.
Highlights
The space of four-dimensional N = 2 superconformal field theories (SCFTs) has a rich structure
The authors of [17] showed that the operator product expansions (OPEs) of a special class of BPS local operators are naturally encoded in a two-dimensional chiral algebra
For some of the OPEs we study in this paper, the three-point function of the corresponding superconformal primary fields turns out to vanish even though three-point functions involving their descendants do not
Summary
Since the Schur operator in the stress tensor multiplet C0(0,0) maps to the Virasoro stress tensor in the associated chiral algebra, the selection rules for (1.2) are important in the study of the 4d/2d correspondence They reveal how the four-dimensional operator associated with a Virasoro primary is related to those of the Virasoro descendants. We find that the sum of the U(1)r charges of Schur operators in these multiplets always vanishes, which suggests that the Schur operators play a central role in Schur multiplets We follow the convention of [17] unless otherwise stated
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