The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators

Abstract

Half BPS correlators in N=4 super Yang-Mills theory are key quantities both in the AdS/CFT correspondence as well as in scattering amplitudes research. They are dual at strong coupling to quantum gravity amplitudes. At weak coupling on the other hand they contain all N=4 SYM amplitudes. They have been found to possess a number of hidden symmetries, for example non-trivial permutation symmetry of perturbative four-point integrands and a higher dimensional conformal symmetry. Their study has enjoyed continuous progress since the discovery of AdS/CFT and they are now some of the best understood quantities of any four-dimensional quantum field theory. In this review we outline the current knowledge of half BPS correlators, emphasising these two co-existing relations to scattering amplitudes at strong and weak coupling.

53 pages, see also the overview article arXiv:2203.13011. v3: journal version

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Cited by in corpus (11)

• The SAGEX Review on Scattering Amplitudes
• Higher-Point Integrands in N=4 super Yang-Mills Theory
• Non-planar integrated correlator in $\mathcal{N}=4$ SYM
• The Kaluza-Klein AdS Virasoro-Shapiro Amplitude near Flat Space
• One-loop string amplitudes in AdS${}_5\times$S${}^5$: Mellin space and sphere splitting
• Notes on conformal integrals: Coulomb branch amplitudes, magic identities and bootstrap
• Four-point correlators in N=4 SYM from AdS${}_5$ bubbling geometries
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
• An Elliptic One-Loop Amplitude in Anti-de-Sitter Space
• Leading singularities and chambers of Correlahedron
• Higher-Point Correlators in N=4 SYM: Generating Functions