A Poincare lemma for sigma models of AKSZ type

TL;DR

This paper demonstrates that for AKSZ-type sigma models, the local BRST cohomology aligns with the target space differential cohomology in local neighborhoods, with implications for gauge systems and the calculus of variations.

Contribution

It establishes an isomorphism between local BRST cohomology and target space differential cohomology for AKSZ sigma models, extending to functional multivectors.

Findings

BRST cohomology matches target space differential cohomology locally

Results apply to the inverse calculus of variations in gauge theories

Provides new tools for analyzing gauge system structures

Abstract

For a sigma model of AKSZ-type, we show that the local BRST cohomology is isomorphic to the cohomology of the target space differential when restricted to coordinate neighborhoods both in the base and in the target. An analogous result is shown to hold for the cohomology in the space of functional multivectors. Applications of these latter cohomology classes in the context of the inverse problem of the calculus of variation for general gauge systems are also discussed.