Higher-spin fermionic gauge fields and their electromagnetic coupling

Abstract

Abstract:We study the electromagnetic coupling of massless higher-spin fermions in flat space. Under the assumptions of locality and Poincaré invariance, we employ the BRST-BV cohomological methods to construct consistent parity-preserving off-shell cubic 1 − s − s vertices. Consistency and non-triviality of the deformations not only rule out minimal coupling, but also restrict the possible number of derivatives. Our findings are in complete agreement with, but derived in a manner independent from, the light-cone-formulation results of Metsaev and the string-theory-inspired results of Sagnotti-Taronna. We prove that any gauge-algebra-preserving vertex cannot deform the gauge transformations. We also show that in a local theory, without additional dynamical higher-spin gauge fields, the non-abelian vertices are eliminated by the lack of consistent second-order deformations.

Consistent interactions and involution

“…There is one identity of the third order l 3 = 1, and no gauge symmetry. Substituting these numbers into the general formula (8) one obtains N = 1 · 1 + 2 · 4 − 3 · 1 = 6 that provides the correct answer, as the massive vector field has 3 physical polarizations, and the physical phase space is 6-dimensional.…”

“…Among the most recent ones we mention the work [8], where all cubic electromagnetic interactions are found by this method for the higher-spin fermionic fields in Minkowski space, and it is proven that the minimal couplings are not admissible.…”

“…With two second order equations (t 2 = 2) and one forth order identity (l 4 = 1), relation (8) brings zero as the number of physical degrees of freedom. Let us directly check that it is a correct count.…”

“…Let us comment on formula (8). At first, we notice that the relation is valid for involutive equations.…”

“…The Conclusion contains a brief discussion of the paper results. In the Appendix we derive the relation (8) which is used in the paper for counting physical degrees of freedom.…”