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

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, Poincaré 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.

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

“…The antifields of the Rarita-Schwinger fields are bosonic, purely imaginary spinors. Like in the previous situations (see [1,2]), the BRST differential simply decomposes into s = δ+γ, where δ represents the Koszul-Tate differential and γ stands for the exterior derivative along the gauge orbits. If we make the notations…”

“…In order to investigate the consistent couplings that can be added to the free action (1) we act like in [1,2] and rely on the reformulation of the interaction problem in the context of the antifield-BRST deformation procedure. Thus, if an interacting gauge theory can be consistently constructed, then the solution S h,ψ to the master equation associated with the free theory, (12), can be deformed into a solutionS h,ψ…”

“…The resolution of equation (14) implies standard cohomological techniques related to the BRST differential of the free model under consideration. The necessary cohomological ingredients have already been discussed in [1,2], so in the sequel we give the solutions to these equations without going into further details. The nontrivial solution to equation (14) can be shown to expand as S h,ψ…”

“…Here, we develop the third step of constructing all possible interactions in D = 11 among a graviton, a massless Majorana spin-3/2 field, and a three-form gauge field. The previous steps were exposed in [1], where we obtained all the interactions that can be added to a eleven-dimensional free theory describing a massless spin-two field and an Abelian three-form gauge field, and respectively in [2], where the same problem was solved with respect to a massless Rarita-Schwinger field and an Abelian three-form gauge field. Based on the previously mentioned results, in the sequel we analyze the consistent couplings that can be introduced between a massless spin-two field (described in the free limit by the Pauli-Fierz action) and a massless Rarita-Schwinger spinor in eleven spacetime dimensions.…”

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…”