Physical and mathematical evidences for a negative-rank tensor
  We propose and study the properties of a new potential demanded by the self-consistency of the duality scheme in electromagnetic-like field theories of totally anti-symmetric tensors in diverse dimensions. Physical implications of this new potential is manifest under the presence of scalar condensates in the Julia-Toulouse mechanism for the nucleation of topological defects with consequences for the confinement phenomenon. 
Patricio Gaete and Clovis Wotzasek