Violation of The Unitarity Bound in a Finite N=8 Theory of Super Gravity

TL;DR

This paper investigates a proposed finite N=8 supergravity theory, revealing that its perturbative amplitudes violate unitarity at high energies, suggesting the need for non-perturbative completion or reevaluation of its finiteness.

Contribution

It critically analyzes the unitarity violation in the perturbative expansion of a candidate finite supergravity theory using both Feynman diagrams and symmetry arguments.

Findings

Perturbative amplitudes violate unitarity at high energies.

Series summation techniques suggest possible non-perturbative unitarity restoration.

The theory's finiteness and unitarity are incompatible without non-perturbative effects.

Abstract

We comment on recent results of a possible finite theory of Super Gravity from both Feynman graph and global E(7,7) symmetry arguments. The four point amplitude can be written as a series in the gravitational coupling and energy squared, Gs, multiplied by coefficient functions of the scattering angle. Every order of the perturbation expansion violates the unitarity bound for any element of the S matrix by powers for large values of the energy. While this conclusion is not unexpected; the meaning of such a theory is not understood. Either the theory is not finite or a non-perturbative completion is necessary. We first review the semi-classical eikonal methods, and then examine Borel techniques to sum the series. Although many details are unknown, we present an example of how an asymptotic behavior that is power bounded and consistent with unitarity might emerge.