A local potential for the Weyl tensor in all dimensions

In all dimensions n ⩾ 4 and arbitrary signature, we demonstrate the existence of a new local potential—a double (2, 3)-form, P ab cde —for the Weyl curvature tensor C abcd , and more generally for all tensors W abcd with the symmetry properties of the Weyl tensor. The classical four-dimensional Lanczos potential for a Weyl tensor—a double (2, 1)-form, H ab c —is proven to be a particular case of the new potential: its double dual.