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arXiv · 2107.01736

The $\sigma_-$ Cohomology Analysis for Symmetric Higher-Spin Fields

A. S. Bychkov·K. A. Ushakov·M. A. Vasiliev
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Abstract

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 $\sigma_-$ 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 $H^p(\sigma_-)$ is computed for any $p$ and interpretation of $H^p(\sigma_-)$ is given both for the original Fronsdal system and for the associated systems of higher form fields.

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A. S. Bychkov, K. A. Ushakov, M. A. Vasiliev. 2021-07-04. The $\sigma_-$ Cohomology Analysis for Symmetric Higher-Spin Fields. https://arxiv.org/abs/2107.01736

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