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.

arXiv comment9 pages, several figures, minor changes

References in corpus (63)

• Deformation quantization of Poisson manifolds, I
• AdS Dual of the Critical O(N) Vector Model
• The Geometry of the Master Equation and Topological Quantum Field Theory
• Introduction to sh Lie algebras for physicists
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Chern-Simons Theory with Vector Fermion Matter
• A path integral approach to the Kontsevich quantization formula
• Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
• Stringy gravity, interacting tensionless strings and massless higher spins
• Constraining conformal field theories with a slightly broken higher spin symmetry
• Particle-Vortex Duality from 3d Bosonization
• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• Conformal Higher Spin Theory
• Light-Front Higher-Spin Theories in Flat Space
• Holography of the N=1 Higher-Spin Theory on AdS4
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
• On the uniqueness of higher-spin symmetries in AdS and CFT
• Effective action in a higher-spin background
• Higher Spin Symmetry and N=4 SYM
• On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations
• Quantum Chiral Higher Spin Gravity
• Higher-Spin Gauge Theories and Bulk Locality
• On limits of superstring in AdS_5 x S^5
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• Light-Front Bootstrap for Chern-Simons Matter Theories
• Chiral Higher Spin Theories and Self-Duality
• More on Quantum Chiral Higher Spin Gravity
• ABJ Triality: from Higher Spin Fields to Strings
• Actions for Self-dual Higher Spin Gravities
• Light-cone gauge cubic interaction vertices for massless fields in AdS(4)
• Exploring the S-Matrix of Massless Particles
• AdS Maps and Diagrams of Bi-local Holography
• A Note on (Non)-Locality in Holographic Higher Spin Theories
• A Derivation of AdS/CFT for Vector Models
• Celestial chiral algebras, colour-kinematics duality and integrability
• A Poincare lemma for sigma models of AKSZ type
• On Effective Field Theories with Celestial Duals
• New Conformal Higher Spin Gravities in $3d$
• First order parent formulation for generic gauge field theories
• The String Dual to Free $\mathcal{N}=4$ Super Yang-Mills
• Conformal higher spin scattering amplitudes from twistor space
• Covariant 4-dimensional fuzzy spheres, matrix models and higher spin
• One-loop Finiteness of Chiral Higher Spin Gravity
• Supersymmetric Higher Spin Theories
• Twistor Constructions for Higher-spin Extensions of (Self-dual) Yang-Mills
• Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
• Spin-Locality of ${\eta }^2$ and ${\bar{\eta }}^2$ Quartic Higher-Spin Vertices
• More on Chiral Higher Spin Gravity and Convex Geometry
• Toward a twistor action for chiral higher-spin gravity
• Minimal models of field theories: Chiral Higher Spin Gravity
• Conformal Higher Spin Theory and Twistor Space Actions
• Gauge PDE and AKSZ-type Sigma Models
• Minimal model of Chiral Higher Spin Gravity
• Manifest Form of the Spin-Local Higher-Spin Vertex ${{\rm Y}}_{\omega CCC}^{\eta \eta }$
• A Twistorial Description of the IKKT-Matrix Model
• Minimal models of field theories: SDYM and SDGR
• Snowmass White Paper: Higher Spin Gravity and Higher Spin Symmetry
• On (spinor)-helicity and bosonization in $Ad{S}_4/CF{T}_3$
• Pre-Calabi-Yau algebras and topological quantum field theories
• The positive Grassmannian, the amplituhedron, and cluster algebras

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