Dimensional reduction as a method to obtain dual theories for massive spin two in arbitrary dimensions

Using the parent Lagrangian method together with a dimensional reduction from D to (D-1) dimensions, we construct dual theories for massive spin two fields in arbitrary dimensions in terms of a mixed symmetry tensor TA[A1A2...AD-2]. Our starting point is the well-studied massless parent action in dimension D. The resulting massive Stueckelberg-like parent actions in (D-1) dimensions inherit all the gauge symmetries of the original massless action and can be gauge fixed in two alternative ways, yielding the possibility of having a parent action with either a symmetric or a nonsymmetric Fierz-Pauli field eAB. Even though the dual sector in terms of the standard spin two field includes only the symmetrical part e(AB) in both cases, these two possibilities yield different results in terms of the alternative dual field TA[A1A2...AD-2]. In particular, the nonsymmetric case reproduces the Freund-Curtright action as the dual to the massive spin two field action in four dimensions.