N=8 Counterterms and E7(7) Current Conservation

TL;DR

This paper demonstrates that all potential counterterms in N=8 supergravity violate E7(7) current conservation, providing evidence for the theory's perturbative ultraviolet finiteness.

Contribution

It proves that N=8 supergravity counterterms at various loop orders are forbidden by E7(7) symmetry, supporting its perturbative UV finiteness.

Findings

4-point counterterms are forbidden at all loop orders by E7(7) current conservation.

n-point counterterms at L=7, 8 are also forbidden due to their relation to 4-point counterterms.

Supports the proof of perturbative UV finiteness of N=8 supergravity.

Abstract

We examine conservation of the E7(7) Noether-Gaillard-Zumino current in the presence of N=8 supergravity counterterms using the momentum space helicity formalism, which significantly simplifies the calculations. The main result is that the 4-point counterterms at any loop order L are forbidden by the E7(7) current conservation identity. We also clarify the relation between linearized and full non-linear superinvariants as candidate counterterms. This enables us to show that all n-point counterterms at L=7, 8 are forbidden since they provide a non-linear completions of the 4-point ones. This supports and exemplifies our general proof in arXiv:1103.4115 of perturbative UV finiteness of N=8 supergravity.