A Theorem on First-Order Interaction Vertices for Free p-Form Gauge Fields

TL;DR

This paper provides a complete proof of a theorem on consistent interactions for free p-form gauge fields, utilizing BRST cohomology, with potential applications to anomaly analysis.

Contribution

It offers the first rigorous proof of a theorem on first-order interaction vertices for free p-form gauge fields, extending to anomaly analysis.

Findings

Proof of the theorem on interaction vertices

Methodology based on local BRST cohomology

Potential applications to anomaly detection

Abstract

The complete proof of a theorem announced in [1] on the consistent interactions for (non-chiral) exterior form gauge fields is given. The theorem can be easily generalized to the analysis of anomalies. Its proof amounts to computing the local BRST cohomology H^0(s|d) in the space of local n-forms depending on the fields, the ghosts, the antifields and their derivatives.