Spin three gauge theory revisited

We study the problem of consistent interactions for spin-3 gauge fields inflat spacetime of arbitrary dimension n>3. Under the sole assumptions ofPoincar\'e and parity invariance, local and perturbative deformation of thefree theory, we determine all nontrivial consistent deformations of the abeliangauge algebra and classify the corresponding deformations of the quadraticaction, at first order in the deformation parameter. We prove that all suchvertices are cubic, contain a total of either three or five derivatives and areuniquely characterized by a rank-three constant tensor (an internal algebrastructure constant). The covariant cubic vertex containing three derivatives isthe vertex discovered by Berends, Burgers and van Dam, which however leads toinconsistencies at second order in the deformation parameter. In dimensions n>4and for a completely antisymmetric structure constant tensor, another covariantcubic vertex exists, which contains five derivatives and passes the consistencytest where the previous vertex failed.Comment: LaTeX, 37 pages. References and comments added. Published versio