Moscow International School of Physics 2022

We propose dual representation for the massless spin 2 theory by the third-rank tensor field with the hook Young diagram. We start from the linearized system of Einstein equations which includes Nordström equation. Once the linearized Nordström equation is a topological field theory, the general solution is a pure gauge. Substituting this general solution into the rest of Einstein system, we arrive at the field equations for the hook tensor, being the initial gauge parameter for the Nordström equation. The degree of freedom count confirms that these higher derivative equations describe massless spin 2 theory. This dual formulation is consistent in any $d\ge3$.