Crossing symmetry for long multiplets in 4D $$ \mathcal{N} $$ = 1 SCFTs

Abstract

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

Defect conformal blocks from Appell functions

“…[36][37][38][39][40][41]. Assuming the successful extension of our work to spinning defect correlators, see previous paragraph, it seems likely that the approach to superconformal blocks we developed in [23,42,43] for bulk four-point functions can be extended to theories with defects. We plan to address this construction in the future.…”

Defect Conformal Blocks from Appell Functions

“…Assuming the successful extension of our work to spinning defect correlators, see previous paragraph, it seems likely that the approach to superconformal blocks we developed in [22,41,42] for bulk four-point functions can be extended to theories with defects. We plan to address this construction in the future.…”