Physical and mathematical evidences for a negative-rank tensor

TL;DR

This paper introduces a new potential in electromagnetic-like theories involving totally anti-symmetric tensors, exploring its physical implications in the context of scalar condensates and topological defect nucleation, with potential relevance to confinement.

Contribution

It presents the theoretical proposal and analysis of a negative-rank tensor potential, expanding the understanding of duality schemes in higher-dimensional field theories.

Findings

Identification of a new potential consistent with duality

Implications for topological defect nucleation and confinement

Connections to scalar condensates in the Julia-Toulouse mechanism

Abstract

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.