BRST cohomology of the Chapline-Manton model

TL;DR

This paper fully computes the local BRST cohomology of the Yang-Mills-2-form system with a Chern-Simons coupling, showing gauge invariance preservation and clarifying anomaly structures including the Green-Schwarz mechanism.

Contribution

It provides a complete cohomological analysis of the Chapline-Manton model, including antifields, and characterizes all consistent anomalies and counterterms.

Findings

Counterterms preserve gauge symmetries.

No new anomalies beyond known ones.

Cohomological interpretation of Green-Schwarz mechanism.

Abstract

We completely compute the local BRST cohomology $H(s|d)$ of the combined Yang-Mills-2-form system coupled through the Yang-Mills Chern-Simons term ("Chapline-Manton model"). We consider the case of a simple gauge group and explicitely include in the analysis the sources for the BRST variations of the fields ("antifields"). We show that there is an antifield independent representative in each cohomological class of $H(s|d)$ at ghost number 0 or 1. Accordingly, any counterterm may be assumed to preserve the gauge symmetries. Similarly, there is no new candidate anomaly beside those already considered in the literature, even when one takes the antifields into account. We then characterize explicitly all the non-trivial solutions of the Wess-Zumino consistency conditions. In particular, we provide a cohomological interpretation of the Green-Schwarz anomaly cancellation mechanism.