Higher-Spin Fermionic Gauge Fields and their Electromagnetic Coupling
We study the electromagnetic coupling of massless higher-spin fermions in flat space. Under the assumptions of locality and Poincar 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 pose restrictions on the possible number of derivatives. Our findings are in complete agreement with the string-field-theoretic results of Sagnotti-Taronna and the light-cone-formulation results of Metsaev. 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.