Gauge fields in (A)dS within the unfolded approach: algebraic aspects

TL;DR

This paper explores the algebraic structure of gauge fields in (A)dS space using the unfolded approach, focusing on the $\sigma_-$-cohomology and its implications for gauge theories.

Contribution

It computes the $\sigma_-$-cohomology for all gauge theories in (A)dS space within the unfolded framework, providing new insights into their algebraic and geometric properties.

Findings

$\sigma_-$-cohomology relates to gauge parameters and fields.

In simple cases, $\sigma_-$-cohomology matches Lie algebra cohomology.

Provides a unified algebraic framework for massless and partially-massless fields.

Abstract

It has recently been shown that generalized connections of the (A)dS space symmetry algebra provide an effective geometric and algebraic framework for all types of gauge fields in (A)dS, both for massless and partially-massless. The equations of motion are equipped with a nilpotent operator called $\sigma_-$ whose cohomology groups correspond to the dynamically relevant quantities like differential gauge parameters, dynamical fields, gauge invariant field equations, Bianchi identities etc. In the paper the $\sigma_-$-cohomology is computed for all gauge theories of this type and the field-theoretical interpretation is discussed. In the simplest cases the $\sigma_-$-cohomology is equivalent to the ordinary Lie algebra cohomology.