On higher-order corrections in M theory

TL;DR

This paper analyzes higher-order corrections to D=11 supergravity within a superspace framework, showing that certain deformations are trivial and deriving the first non-trivial corrections related to anomaly cancellation and field strength modifications.

Contribution

It extends previous cohomology-based analyses to the fully non-linear theory and explicitly constructs the first-order correction terms including anomaly-related deformations.

Findings

Deformations with vanishing lowest-dimensional G_4 component are trivial.

First-order corrections to supergravity equations are derived from anomaly terms.

Supersymmetric completion of the five-brane anomaly term exists and is unique.

Abstract

A theoretical analysis of higher-order corrections to D=11 supergravity is given in a superspace framework. It is shown that any deformation of D=11 supergravity for which the lowest-dimensional component of the four-form $G_4$ vanishes is trivial. This implies that the equations of motion of D=11 supergravity are specified by an element of a certain spinorial cohomology group and generalises previous results obtained using spinorial or pure spinor cohomology to the fully non-linear theory. The first deformation of the theory is given by an element of a different spinorial cohomology group with coefficients which are local tensorial functions of the massless supergravity fields. The four-form Bianchi Identities are solved, to first order and at dimension $-{1/2}$, in the case that the lowest-dimensional component of $G_4$ is non-zero. Moreover, it is shown how one can calculate the first-order correction to the dimension-zero torsion and thus to the supergravity equations of motion given an explicit expression for this object in terms of the supergravity fields. The version of the theory with both a four-form and a seven-form is discussed in the presence of the five-brane anomaly-cancelling term. It is shown that the supersymmetric completion of this term exists and it is argued that it is the unique anomaly-cancelling invariant at this dimension which is at least quartic in the fields. This implies that the first deformation of the theory is completely determined by the anomaly term from which one can, in principle, read off the corrections to all of the superspace field strength tensors.