Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex

Abstract

In the eighties, Berends, Burgers and van Dam (BBvD) found a nonabelian cubic vertex for self-interacting massless fields of spin three in flat spacetime. However, they also found that this deformation is inconsistent at higher order for any multiplet of spin-three fields. For arbitrary symmetric gauge fields, we severely constrain the possible nonabelian deformations of the gauge algebra and, using these results, prove that the BBvD obstruction cannot be cured by any means, even by introducing fields of spin higher (or lower) than three.

19 pages, no figure

References in corpus (3)

• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• Consistent couplings between spin-2 and spin-3 massless fields
• Interacting Higher Spins and the High Energy Limit of the Bosonic String

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