The Ultraviolet Finiteness of N=8 Supergravity

TL;DR

This paper proves that N=8 supergravity in four dimensions is perturbatively UV finite by showing all potential counterterms are invalid in the light-cone superspace, assuming anomaly-free supersymmetry and E7 symmetry.

Contribution

It demonstrates the UV finiteness of N=8 supergravity by ruling out all candidate counterterms through a novel light-cone superspace analysis.

Findings

All candidate counterterms are ruled out in real light-cone superspace.

N=8 supergravity is perturbatively UV finite under certain symmetry assumptions.

The proof generalizes the non-renormalization theorem for N=8 supergravity.

Abstract

We study counterterms (CT's), candidates for UV divergences in the four-dimensional N=8 supergravity. They have been constructed long ago in a Lorentz covariant on shell superspace and recently in the chiral light-cone (LC) superspace. We prove that all of these CT's are ruled out since they are not available in the real LC superspace. This implies the perturbative UV finiteness of d=4 N=8 supergravity under the assumption that supersymmetry and continuous E7 symmetry are anomaly-free. The proof, based on the chiral nature of CT's in the LC superspace, is a generalization of the perturbative F-term non-renormalization theorem for N=8 supergravity.