Tree Amplitudes and Linearized SUSY Invariants in D=11 Supergravity

TL;DR

This paper constructs a linearized supersymmetry-invariant counterterm in D=11 supergravity using tree-level scattering amplitudes, revealing that supersymmetry does not prevent divergences at two loops.

Contribution

It introduces a method to derive the lowest order counterterm in D=11 supergravity from tree-level amplitudes, showing supersymmetry's limitations in protecting against infinities.

Findings

The invariant can be promoted to a two-loop counterterm.

Supersymmetry does not prevent divergences in D=11 supergravity.

Divergence of the 4-graviton amplitude is confirmed.

Abstract

We exploit the tree level bosonic 4-particle scattering amplitudes in D=11 supergravity to construct the bosonic part of a linearized supersymmetry-, coordinate- and gauge-invariant. By differentiation, this invariant can be promoted to be the natural lowest (two-loop) order counterterm. Its existence implies that the perturbative supersymmetry does not protect this ultimate supergravity from infinities, given also the recently demonstrated divergence of its 4-graviton amplitude.