On the uniqueness of D=11 interactions among a graviton, a massless gravitino and a three-form. IV: Putting things together

TL;DR

This paper proves that under certain physical assumptions, the only consistent interactions among specific fields in eleven-dimensional supergravity are those described by N=1, D=11 supergravity.

Contribution

It demonstrates the uniqueness of D=11 supergravity interactions involving a graviton, gravitini, and a 3-form under specified conditions.

Findings

Interactions are uniquely described by N=1, D=11 supergravity.

No other consistent interactions satisfy the hypotheses.

The proof confirms the rigidity of D=11 supergravity structure.

Abstract

Under the hypotheses of smoothness of the interactions in the coupling constant, locality, Poincare invariance, Lorentz covariance, and the preservation of the number of derivatives on each field in the Lagrangian of the interacting theory (the same number of derivatives like in the free Lagrangian), we prove that the only consistent interactions in D=11 among massless gravitini, a graviton, and a 3-form are described by N=1, D=11 SUGRA.