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

TL;DR

This paper proves that in eleven-dimensional spacetime, under certain physical assumptions, there are no interactions between gravitons and gravitini, nor self-interactions among gravitini, contrasting with known results in four dimensions.

Contribution

The work establishes the non-existence of cross-interactions and self-interactions in D=11 supergravity under specific conditions, extending previous theoretical constraints.

Findings

No cross-interactions between graviton and gravitino in D=11

No self-interactions among gravitini in D=11

Comparison indicates differences with D=4 interactions

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 in D=11 there are no cross-interactions between the graviton and the massless gravitino and also no self-interactions in the Rarita-Schwinger sector. A comparison with the case D=4 is briefly discussed.