Consistent deformations of dual formulations of linearized gravity: A no-go result

The consistent, local, smooth deformations of the dual formulation of linearized gravity involving a tensor field in the exotic representation of the Lorentz group with Young symmetry type $(D-3,1)$ (one column of length $D-3$ and one column of length $1)$ are systematically investigated. The rigidity of the Abelian gauge algebra is first established. We next prove a no-go theorem for interactions involving at most two derivatives of the fields.