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.
Highlights
There has been considerable activity recently in the area of computing four-point functions in conformal field theories, motivated by the conformal bootstrap programme initiated in [1]
As an application we 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
The simplest way to do this is to use the Cauchy identity to rewrite the r.h.s. of (4.5) as an infinite sum over the super Schur polynomials. This allows for a direct comparison with the superconformal partial wave (SCPW) expansion and allows us to solve for the OPE coefficients
Summary
There has been considerable activity recently in the area of computing four-point functions in conformal field theories, motivated by the conformal bootstrap programme initiated in [1]. Both to provide further checks as well as to obtain new results, in section 4 we specialise to the case m = n = 2 and use our results to initiate a detailed analysis of mixed charge four-point correlators. We consider four-point functions of scalar operators of arbitrary weight on the Grassmannian and in particular obtain the (super) conformal partial wave associated with any operator occurring in the OPE of two of them. We will obtain explicit formulae for the partial waves, both as an expansion in Schur polynomials with given coefficients, and in a summed up form
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
