Superconformal partial waves in Grassmannian field theories

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=4N=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=4N=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.