More on Chiral Higher Spin Gravity and Convex Geometry

Abstract

Recently, a unique class of local Higher Spin Gravities with propagating massless fields in $4d$ - Chiral Higher Spin Gravity - was given a covariant formulation both in flat and $(A)d{S}_4$ spacetimes at the level of equations of motion. We unfold the corresponding homological perturbation theory as to explicitly obtain all interaction vertices. The vertices reveal a remarkable simplicity after an appropriate change of variables. Similarly to formality theorems the $A_{\infty }/L_{\infty }$ multi-linear products can be represented as integrals over a configuration space, which in our case is the space of convex polygons. The $A_{\infty }$-algebra underlying Chiral Theory is of pre-Calabi-Yau type. As a consequence, the equations of motion have the Poisson sigma-model form.

arXiv comment41 pages + Appendices + Biblio = 61 pages

References in corpus (36)

• 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
• Massless Higher Spins and Holography
• Chern-Simons Theory with Vector Fermion Matter
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
• Conformal Higher Spin Theory
• Light-Front Higher-Spin Theories in Flat Space
• 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
• Static BPS black hole in 4d higher-spin gauge theory
• 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
• An Exact Solution of 4D Higher-Spin Gauge Theory
• Chiral Higher Spin Theories and Self-Duality
• More on Quantum Chiral Higher Spin Gravity
• Light-cone gauge cubic interaction vertices for massless fields in AdS(4)
• AdS Maps and Diagrams of Bi-local Holography
• A Note on (Non)-Locality in Holographic Higher Spin Theories
• On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
• Covariant 4-dimensional fuzzy spheres, matrix models and higher spin
• Homotopy Properties and Lower-Order Vertices in Higher-Spin Equations
• Formal Higher Spin Gravities
• Hochschild cohomology of the Weyl algebra and traces in deformation quantization
• Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
• FRW and domain walls in higher spin gravity
• Manifest Form of the Spin-Local Higher-Spin Vertex ${{\rm Y}}_{\omega CCC}^{\eta \eta }$
• Pre-Calabi-Yau algebras and double Poisson brackets
• Characteristic Cohomology and Observables in Higher Spin Gravity
• Planar solutions of higher-spin theory. Nonlinear corrections
• Planar solutions of higher-spin theory I: free field level

Cited by in corpus (5)

• Chiral Higher Spin Gravity and Convex Geometry
• On correlation functions as higher-spin invariants
• Massless chiral fields in six dimensions
• Four-point functions and contact terms from higher-spin Ward identities of Chern-Simons-matter theory
• Unfolded hypermultiplet in harmonic superspace