Crossing Symmetry for Long Multiplets in 4D $\mathcal{N}=1$ SCFTs

TL;DR

This paper develops crossing symmetry equations for mixed correlators involving long and BPS operators in 4D $ calN=1$ SCFTs, providing explicit formulas and new constraints on operator product expansion data.

Contribution

It introduces a group theoretic approach to derive explicit crossing equations for long multiplets in 4D $ calN=1$ SCFTs, including new constraints beyond previous analyses.

Findings

Derived four crossing symmetry equations for mixed correlators.

Reproduced known equations and introduced three new constraints.

Provided explicit superconformal block expressions for practical use.

Abstract

In this work we construct the crossing symmetry equations for mixed correlators of two long and two BPS operators in 4D $\mathcal{N}=1$ 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.