The consistent interactions between a single, free, massless tensor gauge field with the mixed symmetry (3,1) and an Abelian p-form are investigated in the framework of the BRST formalism combined with cohomological techniques. Under the assumptions on smoothness, locality, Lorentz covariance, and Poincar\'{e} invariance of the deformations, supplemented by the requirement that the interacting Lagrangian is at most second-order derivative, it is proved that for every value p≥1 of the form degree there are consistent couplings between the Abelian form and the massless (3,1) gauge field.
@article{arxiv.hep-th/0702018,
title = {Generalized couplings between an Abelian $p$-form and a (3,1) mixed symmetry tensor field},
author = {C. C. Ciobirca and S. O. Saliu},
journal= {arXiv preprint arXiv:hep-th/0702018},
year = {2007}
}