Higher-Spin Fermionic Gauge Fields and Their Electromagnetic Coupling

TL;DR

This paper investigates the electromagnetic interactions of massless higher-spin fermions in flat space, using cohomological methods to identify consistent cubic vertices and analyze their gauge properties.

Contribution

It provides a cohomological construction of cubic interaction vertices for higher-spin fermions, showing restrictions on minimal coupling and gauge deformation possibilities.

Findings

Minimal coupling is ruled out by consistency conditions.

Non-abelian vertices cannot deform gauge transformations.

Non-abelian vertices are eliminated without additional dynamical fields.

Abstract

We study the electromagnetic coupling of massless higher-spin fermions in flat space. Under the assumptions of locality and Poincare 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.