Covariant action for conformal higher spin gravity

TL;DR

This paper introduces a covariant, background-independent action for conformal higher spin gravity, utilizing deformation quantization and Fedosov's approach to achieve gauge invariance and global well-definedness.

Contribution

It presents a novel covariant action formulation for conformal higher spin gravity based on deformation quantization and Fedosov's method, extending previous models.

Findings

Provides a background-independent reformulation of conformal higher spin fields.

Achieves a gauge-invariant, globally well-defined action functional.

Connects the theory with topological quantum mechanics via the worldline approach.

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.