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Superconformal partial waves in Grassmannian field theories.

Doobary, Reza and Heslop, Paul (2015) 'Superconformal partial waves in Grassmannian field theories.', Journal of high energy physics., 2015 (12). p. 159.


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.

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Publisher statement:This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Date accepted:06 December 2015
Date deposited:30 March 2016
Date of first online publication:23 December 2015
Date first made open access:No date available

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