Consistent Interactions Involving Dual Formulations of Linearized Gravity in Terms of Massless Tensor Fields with the Mixed Symmetry (k,1)

Nontrivial consistent interactions of a single massless tensor field with the mixed symmetry corresponding to a two-column Young diagram (k,1) with k>3, dual to linearized gravity in D=k+3 space-time dimensions, are studied in the following cases: self-couplings, cross-interactions with a Pauli-Fierz field, cross-couplings to purely matter theories, interactions with an Abelian p-form, and couplings with a massless tensor field with the mixed symmetry (m, m) (yet another dual formulation of linearized gravity). Our approach is based on the deformation of the solution to the master equation from the antifield-BRST formalism by means of the local cohomology of the BRST differential. Our main results are obtained under the assumptions that the emerging interactions are local in space-time, analytical in the deformation parameter, Lorentz-covariant, Poincare-invariant, and of maximum derivative order equal to two.