Superconformal partial waves in Grassmannian field theories

Doobary, Reza; Heslop, Paul

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.

Citation

Doobary, R., & Heslop, P. (2015). Superconformal partial waves in Grassmannian field theories. Journal of High Energy Physics, 2015(12), Article 159. https://doi.org/10.1007/jhep12%282015%29159

• Journal Article Type: Article
• Acceptance Date: Dec 6, 2015
• Online Publication Date: Dec 23, 2015
• Publication Date: Dec 1, 2015
• Deposit Date: Jan 5, 2016
• Publicly Available Date: Mar 30, 2016
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2015
• Issue: 12
• Article Number: 159
• DOI: https://doi.org/10.1007/jhep12%282015%29159
• Public URL: https://durham-repository.worktribe.com/output/1423906
• Related Public URLs: http://arxiv.org/abs/arXiv:1508.03611