Crossing symmetry for long multiplets in 4D N=1 SCFTs

In this work we construct the crossing symmetry equations for mixed correlators of two long and two BPS operators in 4D N = 1 SCFTs. The analysis presented here illustrates how our general group theoretic approach to long superblocks and tensor structures of superconformal algebras can be applied to give explicit ready-to-use expressions. In the case at hand, we obtain a system of four crossing symmetry equations for the relevant OPE coefficients. One of these four equations coincides with the equation found and analysed by Li, Meltzer and Stergiou by restricting to the superprimary component of the long multiplets. The other three equations are new and they provide powerful additional constraints on the same OPE data.

Automated summary

In this work, we constructed crossing symmetry equations for mixed correlators of two long and two BPS operators in 4D N = 1 SCFTs. The analysis demonstrates the application of a general group theoretic approach to long superblocks and tensor structures of superconformal algebras, providing explicit expressions for OPE coefficients. The system of four crossing symmetry equations obtained in this case includes one previously analyzed equation and three new equations that offer additional constraints on the OPE data.