Chiral higher spin gravity and convex geometry

Sharapov, A. A.; Skvortsov, Evgeny; Dongen, Richard van

doi:10.21468/scipostphys.14.6.162

Cited by 7 publications

(2 citation statements)

References 89 publications

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“…It is quite amusing that the action of CHS gravity requires such advanced constructions from deformation quantization as Shoikhet-Tsygan-Kontsevich formality that gives a proper measure for the invariant trace on the algebra of quantum observables, using the Feigin-Felder-Shoikhet cocycle. Somewhat related links to the same formality have already been observed [105], in particular, for Chiral HS gravity [106][107][108].…”

Section: Conclusion and Discussionsupporting

confidence: 70%

Covariant action for conformal higher spin gravity

Basile,

Grigoriev,

Skvortsov

2023

J. Phys. A: Math. Theor.

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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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Section: Conclusion and Discussionsupporting

confidence: 70%

Covariant action for conformal higher spin gravity

Basile,

Grigoriev,

Skvortsov

2023

J. Phys. A: Math. Theor.

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“…Chiral higher spin theory [83,115,116] in flat space in the light cone gauge contains only cubic vertices. However, in AdS, it can contain vertices of all orders.…”

Section: Chiral Higher Spin Theorymentioning

confidence: 99%

Constraining momentum space correlators using slightly broken higher spin symmetry

Jain

John

Malvimat

2021

J. High Energ. Phys.

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In this work, building up on [1] we present momentum space Ward identities related to broken higher spin symmetry as an alternate approach to computing correlators of spinning operators in interacting theories such as the quasi-fermionic and quasi-bosonic theories. The direct Feynman diagram approach to computing correlation functions is intricate and in general has been performed only in specific kinematic regimes. We use higher spin equations to obtain the parity even and parity odd contributions to two-, three- and four-point correlators involving spinning and scalar operators in a general kinematic regime, and match our results with existing results in the literature for cases where they are available.One of the interesting facts about higher spin equations is that one can use them away from the conformal fixed point. We illustrate this by considering mass deformed free boson theory and solving for two-point functions of spinning operators using higher spin equations.

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Strong homotopy algebras for chiral higher spin gravity via Stokes theorem

Sharapov,

Skvortsov,

Van Dongen

2024

J. High Energ. Phys.

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Chiral higher spin gravity is defined in terms of a strong homotopy algebra of pre-Calabi-Yau type (noncommutative Poisson structure). All structure maps are given by the integrals over the configuration space of concave polygons and the first two maps are related to the (Shoikhet-Tsygan-)Kontsevich Formality. As with the known formality theorems, we prove the A∞-relations via Stokes’ theorem by constructing a closed form and a configuration space whose boundary components lead to the A∞-relations. This gives a new way to formulate higher spin gravities and hints at a construct encompassing the known formality theorems.

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Chiral higher spin gravity and convex geometry

Cited by 7 publications

References 89 publications

Covariant action for conformal higher spin gravity

Covariant action for conformal higher spin gravity

Constraining momentum space correlators using slightly broken higher spin symmetry

Strong homotopy algebras for chiral higher spin gravity via Stokes theorem

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