Tree Amplitudes and Two-loop Counterterms in D=11 Supergravity

TL;DR

This paper calculates four-particle scattering amplitudes in D=11 supergravity, revealing a potential two-loop counterterm that indicates the theory's nonrenormalizability despite supersymmetry protections.

Contribution

It constructs a linearized supersymmetry- and gauge-invariant on-shell amplitude and identifies a local counterterm candidate at two loops in D=11 supergravity.

Findings

Explicit four-particle amplitude calculation in D=11 supergravity

Identification of a two-loop counterterm candidate

Demonstration that supersymmetry does not prevent nonrenormalizability

Abstract

We compute the tree level 4-particle bosonic scattering amplitudes in D=11 supergravity. By construction, they are part of a linearized supersymmetry-, coordinate- and 3-form gauge-invariant. While this on-shell invariant is nonlocal, suitable SUSY-preserving differentiations turn it into a local one with correct dimension to provide a natural lowest (two-loop) order counterterm candidate. Its existence shows explicitly that no symmetries protect this ultimate supergravity from the nonrenormalizability of its lower-dimensional counterparts.