On the uniqueness of D=11 interactions among a graviton, a massless gravitino and a three-form. I: Pauli-Fierz and three-form

TL;DR

This paper investigates the unique consistent interactions between a graviton and a three-form gauge field in eleven dimensions, confirming their singular form as prescribed by General Relativity using BRST cohomology methods.

Contribution

It demonstrates the uniqueness of D=11 interactions between a graviton and a three-form through a cohomological deformation approach.

Findings

Confirmed the uniqueness of the interaction in D=11

Derived the interaction under locality and Lorentz invariance constraints

Supported the form of interactions prescribed by General Relativity

Abstract

Cross-couplings between a massless spin-two field (described in the free limit by the Pauli-Fierz action) and an Abelian three-form gauge field in D=11 are investigated in the framework of the deformation theory based on local BRST cohomology. These consistent interactions are obtained on the grounds of smoothness in the coupling constant, locality, Lorentz covariance, Poincare invariance, and the presence of at most two derivatives in the interacting Lagrangian. Our results confirm the uniqueness of the eleven-dimensional interactions between a graviton and a three-form prescribed by General Relativity.