From lightcone actions to maximally supersymmetric amplitudes

TL;DR

This paper develops lightcone superspace actions for N=4 SYM and N=8 supergravity, enabling recursive amplitude calculations and exploring their relation through the double-copy property.

Contribution

It introduces new lightcone superspace actions for these theories, simplifying amplitude computations and elucidating their connection via the double-copy framework.

Findings

Recursive MHV amplitude calculations match known results.

Supergravity cubic vertex is the square of the gauge theory vertex.

Connections to BCFW recursion relations are established.

Abstract

In this article actions for N=4 SYM and N=8 supergravity are formulated in terms of a chiral superfield, which contains only the physical degrees of freedom of either theory. In these new actions, which originate from the lightcone superspace, the supergravity cubic vertex is the square of the gauge theory one (omitting the color structures). Amplitude calculations using the corresponding Feynman supergraph rules are tedious, but can be simplified by choosing a preferred superframe. Recursive calculations of all MHV amplitudes in N=4 SYM and the four-point N=8 supergravity amplitude are shown to agree with the known results and connections to the BCFW recursion relations are pointed out. Finally, the new path integrals are discussed in the context of the double-copy property relating N=4 SYM theory to N=8 supergravity.