Inconsistency of point-particle dynamics on higher-spin backgrounds

Vyacheslav Ivanovskiy; Dmitry Ponomarev

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arXiv · 2503.11546

Inconsistency of point-particle dynamics on higher-spin backgrounds

Vyacheslav Ivanovskiy·Dmitry Ponomarev

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Abstract

We use the light-cone gauge formalism to study interactions of point particles with massless higher-spin fields. By analysing the light-cone consistency conditions at the subleading order in higher-spin fields, we find that no local interactions of point particles with chiral higher-spin fields are possible. Considering that chiral higher-spin theories form inevitable closed subsectors of any consistent massless higher-spin theories in flat space, this conclusion holds more generally, in particular, it applies to putative parity-invariant completions of chiral higher-spin theories. Besides that, we argue that our result implies that Riemannian geometry cannot be extended to spaces with non-trivial higher-spin fields, in particular, there is no higher-spin extension of space-time interval. In the present paper we focus on a case of a massless particle, while a more technical massive case will be analysed in a companion paper.

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Vyacheslav Ivanovskiy, Dmitry Ponomarev. 2025-06-26. Inconsistency of point-particle dynamics on higher-spin backgrounds. https://arxiv.org/abs/2503.11546

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