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=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.
Cite
@article{arxiv.1508.03611,
title = {Superconformal partial waves in Grassmannian field theories},
author = {Reza Doobary and Paul Heslop},
journal= {arXiv preprint arXiv:1508.03611},
year = {2016}
}
Comments
Minor corrections and a new subsection 3.5.1 giving explicit forms for the superconformal partial waves in N=4 SYM in terms of one- and two-variable functions for easier comparison with other approaches