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.

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

References in corpus (2)

• N=4 Superconformal Characters and Partition Functions
• A note on four-point correlators of half-BPS operators in N=4 SYM

Cited by in corpus (19)

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• One-loop amplitudes in $Ad{S}_5\times S^5$ supergravity from $\mathcal{N}=4$ SYM at strong coupling
• All three-loop four-point correlators of half-BPS operators in planar N=4 SYM
• String corrections to AdS amplitudes and the double-trace spectrum of N=4 SYM
• Modular invariant holographic correlators for $\mathcal{N}=4$ SYM with general gauge group
• Bootstrapping line defects in $\mathcal{N}=2$ theories
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• On correlation functions of BPS operators in $3d$ $\mathcal{N}=6$ superconformal theories
• BCJ relations in ${AdS}_5\times S^3$ and the double-trace spectrum of super gluons
• Two-particle spectrum of tensor multiplets coupled to $Ad{S}_3\times S^3$ gravity
• Perturbative Four-Point Functions from the Analytic Conformal Bootstrap
• Higher-Dimensional Symmetry of AdS${}_2\times$S${}^2$ Correlators
• Bootstrapping string theory on AdS${}_5\times S^5$
• Superconformal blocks in diverse dimensions and $BC$ symmetric functions
• Interactions as conformal intertwiners in 4D QFT
• Harmonic Analysis in d-dimensional Superconformal Field Theory