On the uniqueness of D=11 interactions among a graviton, a massless gravitino and a three-form. II: Three-form and gravitini

TL;DR

This paper proves that under certain physical and mathematical conditions, no new interactions or self-couplings exist between a graviton, gravitino, and three-form in eleven dimensions, except for a Chern-Simons term for the three-form.

Contribution

It demonstrates the non-existence of cross-couplings and gravitino self-interactions in D=11 under specified assumptions, except for a Chern-Simons term for the three-form.

Findings

No cross-couplings or gravitino self-interactions in D=11.

Only a Chern-Simons term for the three-form can be added.

The results are based on BRST cohomology and deformation analysis.

Abstract

The interactions that can be introduced between a massless Rarita-Schwinger field and an Abelian three-form gauge field in eleven spacetime dimensions are analyzed in the context of the deformation of the free solution of the master equation combined with local BRST cohomology. Under the hypotheses of smoothness of the interactions in the coupling constant, locality, Poincare invariance, Lorentz covariance, and the presence of at most two derivatives in the Lagrangian of the interacting theory (the same number of derivatives like in the free Lagrangian), we prove that there are neither cross-couplings nor self-interactions for the gravitino in D=11.The only possible term that can be added to the deformed solution to the master equation is nothing but a generalized Chern-Simons term for the three-form gauge field, which brings contributions to the deformed Lagrangian, but does not modify the original, Abelian gauge transformations.