Chiral Higher Spin Gravity and Convex Geometry

Abstract

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 $3d$ bosonization duality. In this letter, we explicitly construct an $A_{\infty }$-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.

9 pages, several figures, minor changes

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Cited by in corpus (4)

• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• Massless chiral fields in six dimensions
• Four-point functions and contact terms from higher-spin Ward identities of Chern-Simons-matter theory
• All actions for free massive higher-spin fields