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Under the hypotheses of smoothness in the coupling constant, locality,Lorentz covariance, and Poincare invariance of the deformations, combined withthe preservation of the number of derivatives on each field, the consistentinteractions between a single free massless tensor gauge field with the mixedsymmetry of a two-column Young diagram of the type (3,1) and one Abelian vectorfield have been investigated. The computations are done with the help of thedeformation theory based on a cohomological approach, in the context of theantifield-BRST formalism. The main result is that there exist nontrivialcross-couplings between these types of fields in five spatiotemporaldimensions, which break the PT invariance and allow for the deformation of thegauge transformations of the vector field, but not of the gauge algebra.

Couplings between a single massless tensor field with the mixed symmetry (3,1) and one vector field