The \(\sigma_-\) 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...

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Bibliographic Details
Published in:arXiv.org 2024-08
Main Authors: Bychkov, A S, Ushakov, K A, Vasiliev, M A
Format: Article
Language:English
Subjects:
Homology
Integers
Minkowski space
Tensors
Online Access:Get full text
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Summary: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.
ISSN:2331-8422