More on Chiral Higher Spin Gravity and convex geometry

Sharapov, A. A.; Skvortsov, Evgeny; Sukhanov, Arseny; Dongen, Richard Van

doi:10.1016/j.nuclphysb.2023.116152

Cited by 9 publications

(4 citation statements)

References 67 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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“…|Q| depends on Q modulo cyclic permutations of the columns. The configuration space n can also be understood as a subset in the oriented Grassmannian Gr(2, n), with q i j being the corresponding Plücker's coordinates [49]. It is not a positive one [50,51], but the signs of q i j are fixed.…”

Section: Configuration Space and Convex Geometrymentioning

confidence: 99%

“…However, the products obtained this way are very complicated and do not immediately reveal neither the relation to convex geometry nor to pre-Calabi-Yau algebras. The details of the derivation will be given elsewhere[88].…”

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confidence: 99%

Chiral higher spin gravity and convex geometry

2023

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Chiral Higher Spin Gravity is the minimal extension of the graviton with propagating massless higher spin fields. It admits any value of the cosmological constant, including zero. Its existence implies that Chern-Simons vector models have closed subsectors and supports the 3d3d bosonization duality. In this letter, we explicitly construct an A_\inftyA∞-algebra that determines all interaction vertices of the theory. The algebra turns out to be of pre-Calabi-Yau type. The corresponding products, some of which originate from Shoikhet-Tsygan-Kontsevich formality, are given by integrals over the configuration space of convex polygons.

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“…Fortunately, the key features of the higher-spin symmetry (such as mixing spins and derivatives) that generically invalidate the field theory approach are harmless on the CFT side. It should be mentioned that the dual theory has a closed local subsector [47][48][49][50][51], which is an AdS 4 -deformation of the chiral higher-spin gravity in flat space [52][53][54][55][56][57][58][59], see, e.g., ref. [60] for more on higher-spin gravities.…”

Section: Introductionmentioning

confidence: 99%