The $σ_-$ Cohomology Analysis for Symmetric Higher-Spin Fields
In this paper, we present a complete proof of the so-called First On-Shell Theorem that determines dynamical content of the unfolded equations for free symmetric massless fields of arbitrary integer spin in any dimension and arbitrary integer or half-integer spin in four dimensions. This is achieved by calculation of the respective $σ_-$ cohomology both in the tensor language in Minkowski space of any dimension and in terms of spinors in $AdS_4$. In the $d$-dimensional case $H^p(σ_-)$ is computed for any $p$ and interpretation of $H^p(σ_-)$ is given both for the original Fronsdal system and for the associated systems of higher form fields.
hep-th↗