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

TL;DR

This review discusses half BPS correlators in N=4 super Yang-Mills theory, highlighting their duality with quantum gravity amplitudes at strong coupling and their relation to scattering amplitudes at weak coupling, emphasizing their symmetries and progress.

Contribution

It provides a comprehensive overview of the current understanding of half BPS correlators, focusing on their dualities and hidden symmetries in N=4 SYM.

Findings

Revealed permutation symmetry in perturbative integrands

Identified higher-dimensional conformal symmetry

Summarized progress in understanding 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.