Characteristic cohomology of $p$-form gauge theories

TL;DR

This paper explicitly computes the characteristic cohomology for free and interacting p-form gauge theories, revealing its finite-dimensional structure and generators, with implications for BRST cohomology.

Contribution

It provides a complete calculation of characteristic cohomology for p-form gauge fields, including interactions, extending previous understanding and linking to BRST cohomology.

Findings

Characteristic cohomology is finite-dimensional.

Generated by forms dual to field strengths.

Extended to interacting theories with gauge invariant interactions.

Abstract

The characteristic cohomology $H^k_{char}(d)$ for an arbitrary set of free $p$-form gauge fields is explicitly worked out in all form degrees $k<n-1$, where $n$ is the spacetime dimension. It is shown that this cohomology is finite-dimensional and completely generated by the forms dual to the field strengths. The gauge invariant characteristic cohomology is also computed. The results are extended to interacting $p$-form gauge theories with gauge invariant interactions. Implications for the BRST cohomology are mentioned.