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arXiv · 2212.10336

Covariant action for conformal higher spin gravity

Thomas Basile·Maxim Grigoriev·Evgeny Skvortsov
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Abstract

Conformal Higher Spin Gravity is a higher spin extension of Weyl gravity and is a family of local higher spin theories, which was put forward by Segal and Tseytlin. We propose a manifestly covariant and coordinate-independent action for these theories. The result is based on an interplay between higher spin symmetries and deformation quantization: a locally equivalent but manifestly background-independent reformulation, known as the parent system, of the off-shell multiplet of conformal higher spin fields (Fradkin-Tseytlin fields) can be interpreted in terms of Fedosov deformation quantization of the underlying cotangent bundle. This brings into the game the invariant quantum trace, induced by the Feigin-Felder-Shoikhet cocycle of Weyl algebra, which extends Segal's action into a gauge invariant and globally well-defined action functional on the space of configurations of the parent system. The same action can be understood within the worldline approach as a correlation function in the topological quantum mechanics on the circle.

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Thomas Basile, Maxim Grigoriev, Evgeny Skvortsov. 2022-12-20. Covariant action for conformal higher spin gravity. https://arxiv.org/abs/2212.10336

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