On the Uniqueness of D = 11 Interactions Among a Graviton, a Massless Gravitino and a Three-Form I: Pauli–fierz and Three-Form

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, Poincaré 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.

On the Uniqueness of D = 11 Interactions Among a Graviton, a Massless Gravitino and a Three-Form Ii: Three-Form and Gravitini

“…(More details of the various graduations of the BRST generators can be found in Ref. [1].) In agreement with the standard rules of the BRST formalism, the degrees of the BRST generators are valued like…”

“…Since the gauge generators of the free theory under study are field independent, it follows that the BRST differential decomposes again like in Ref. [1]…”

“…The fact that the gauge transformations of the three-form gauge field are off-shell, second-order reducible is treated in more detail in Ref. [1]. In order to construct the BRST symmetry for (1) we introduce the field, ghost, and antifield spectra…”

“…With this purpose in mind, in Ref. [1] we have obtained all consistent interactions that can be added to a free theory describing a massless spin-two field and an Abelian three-form gauge field in eleven spacetime dimensions. Here, we develop the second step of our approach and analyze the consistent eleven-dimensional interactions that can be introduced between a massless Rarita-Schwinger field and an Abelian three-form gauge field.…”

On the consistent interactions in D = 11 among a graviton, a massless gravitino and a three‐form

“…We have shown in [6][7][8][9] that the first-order deformation S 1 can be decomposed as a sum of six components…”