Geometry of the non-Abelian 2-index potential and twisted de Rham cohomology

TL;DR

This paper explores the geometric structure of the non-Abelian 2-index potential, revealing its relation to twisted de Rham cohomology, and proposes a non-Abelian extension of S-duality under certain conditions.

Contribution

It demonstrates that the non-Abelian 2-index potential aligns with twisted de Rham cohomology and introduces a non-Abelian generalization of S-duality.

Findings

The 2-index potential fits into twisted de Rham cohomology framework.

Results on the Euler characteristic of the twisted de Rham complex.

Proposal of a non-Abelian S-duality under specific conditions.

Abstract

It is found that the 2-index potential in nonabelian theories does not behave geometrically as a connection but that, considered as an element of the second de Rham cohomology group twisted by a flat connection, it fits well with all the properties assigned to it in various physical contexts. We also prove some results on the Euler characteristic of the twisted de Rham complex. Finally, provided that some conditions are satisfied, we propose a non-Abelian generalisation of S-duality.