Superconformal partial waves in Grassmannian field theories

We derive superconformal partial waves for all scalar four-point functions on a super Grassmannian space Gr(m vertical bar n, 2m vertical bar 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(2 n) 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.