The Correlahedron

Eden, Burkhard; Heslop, Paul; Mason, Lionel

Abstract

We introduce a new geometric object, the correlahedron, which we conjecture to be equivalent to stress-energy correlators in planar N=4N=4 super Yang-Mills. Re-expressing the Grassmann dependence of correlation functions of n chiral stress-energy multiplets with Grassmann degree 4k in terms of 4(n + k)-linear bosonic variables, the resulting expressions have an interpretation as volume forms on a Gr(n+k, 4+n+k) Grassmannian, analogous to the expressions for planar amplitudes via the amplituhedron. The resulting volume forms are to be naturally associated with the correlahedron geometry. We construct such expressions in this bosonised space both directly, in general, from Feynman diagrams in twistor space, and then more invariantly from specific known correlator expressions in analytic superspace. We give a geometric interpretation of the action of the consecutive lightlike limit and show that under this the correlahedron reduces to the squared amplituhedron both as a geometric object as well as directly on the corresponding volume forms. We give an explicit easily implementable algorithm via cylindrical decompositions for extracting the squared amplituhedron volume form from the squared amplituhedron geometry with explicit examples and discuss the analogous procedure for the correlators.

Citation

Eden, B., Heslop, P., & Mason, L. (2017). The Correlahedron. Journal of High Energy Physics, 2017(9), Article 156. https://doi.org/10.1007/jhep09%282017%29156

• Journal Article Type: Article
• Acceptance Date: Sep 16, 2017
• Online Publication Date: Sep 28, 2017
• Publication Date: Sep 28, 2017
• Deposit Date: Sep 7, 2017
• Publicly Available Date: Oct 6, 2017
• 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: 2017
• Issue: 9
• Article Number: 156
• DOI: https://doi.org/10.1007/jhep09%282017%29156
• Public URL: https://durham-repository.worktribe.com/output/1349762
• Related Public URLs: http://arxiv.org/pdf/1701.00453.pdf