N=8 Supergravity on the Light Cone

TL;DR

The paper develops a generating functional for N=8 supergravity amplitudes in light-cone superspace using an unconstrained chiral superfield, connecting LC amplitudes to Nair-type covariant constructions. It argues that quantum corrections yield non-local transverse structures, which suppress UV divergences and, when combined with the non-linear E7(7) symmetry and SUSY recursion relations, lead to an all-loop finiteness prediction in d=4. The framework preserves manifest kinematical supersymmetry while non-linear symmetries govern higher-point consistency, and it provides a path to test these predictions via explicit LC supergraph calculations and dimensional extensions. The work also discusses non-perturbative implications for extremal black holes and outlines concrete near-term tasks to validate the generating functional against known amplitudes and artifacts of dimension-changing analyses.

Abstract

We construct the generating functional for the light-cone superfield amplitudes in a chiral momentum superspace. It generates the n-point particle amplitudes which on shell are equivalent to the covariant ones. Based on the action depending on unconstrained light-cone chiral scalar superfield, this functional provides a regular d=4 QFT path integral derivation of the Nair-type amplitude constructions. By performing a Fourier transform into the light-cone chiral coordinate superspace we find that the quantum corrections to the superfield amplitudes with n legs are non-local in transverse directions for the diagrams with the number of loops smaller than n(n-1)/2 +1. This suggests the reason why UV infinities, which are proportional to local vertices, cannot appear at least before 7 loops in the light-cone supergraph computations. By combining the E7 symmetry with the supersymmetric recursion relations we argue that the light-cone supergraphs predict all loop finiteness of d=4 N=8 supergravity.