Obstruction to E_{7(7)} Deformation in N=8 Supergravity

TL;DR

This paper demonstrates that it is impossible to deform N=8 supergravity to restore E_{7(7)} duality while preserving both supersymmetry and general covariance, due to the necessity of higher spins and multiple gravitons.

Contribution

It provides a proof that extending the E_{7(7)} duality deformation to the full N=8 supergravity theory is not feasible without introducing higher spins and multiple gravitons.

Findings

Deformation of N=8 supergravity to restore duality is impossible under current constraints.

Restoring E_{7(7)} duality requires higher spins and multiple gravitons.

The proposed deformation scheme cannot be extended to the full theory.

Abstract

Candidate counterterms break Noether-Gaillard-Zumino E_{7(7)} current conservation in N=8 supergravity in four dimensions. Bossard and Nicolai proposed a scheme for deforming the subsector involving vector fields in a Lorentz covariant manner, so as to restore duality. They argued that there must exist an extension of this deformation to the full theory that preserves supersymmetry. We show that it is not possible to deform the maximal supergravity to restore E_{7(7)} duality, while maintaining both general covariance and N=8 supersymmetry, as was proposed. Deformation of N=8 supergravity requires higher spins and multiple gravitons, which presents a concrete obstacle to this proposal.