Superconformal partial waves in Grassmannian field theories

TL;DR

This paper derives superconformal partial waves for scalar four-point functions across various super Grassmannian spaces, enabling detailed analysis of protected and unprotected sectors in superconformal field theories like N=4 SYM.

Contribution

It provides a comprehensive derivation of superconformal partial waves applicable to multiple theories and spaces, including new insights into protected sectors in N=4 SYM.

Findings

Separation of protected and unprotected sectors in four-point functions.

Prediction of a protected twist four sector in <3333> correlator.

Complete determination of protected twist four operators for each spin.

Abstract

We derive superconformal partial waves for all scalar four-point functions on a super Grassmannian space Gr(m|n,2m|2n) for all m,n. This family of four-point functions includes those of all (arbitrary weight) half BPS operators in both N=4 SYM (m=n=2) and in N=2 superconformal field theories in four dimensions (m=2,n=1) on analytic superspace. It also includes four-point functions of all (arbitrary dimension) scalar fields in non-supersymmetric conformal field theories (m=2,n=0) on Minkowski space, as well as those of a certain class of representations of the compact SU(2n) coset spaces. As an application we then specialise to N=4 SYM and use these results to perform a detailed superconformal partial wave analysis of the four- point functions of arbitrary weight half BPS operators. We discuss the non-trivial separation of protected and unprotected sectors for the <2222>, <2233> and <3333> cases in an SU(N) gauge theory at finite N. The <2233> correlator predicts a non-trivial protected twist four sector for <3333> which we can completely determine using the knowledge that there is precisely one such protected twist four operator for each spin.