Minimal models of field theories: Chiral Higher Spin Gravity

Abstract

There exists a unique class of local Higher Spin Gravities with propagating massless fields in $4d$ - Chiral Higher Spin Gravity. Originally, it was formulated in the light-cone gauge. We construct a covariant form of this theory as a Free Differential Algebra up to NLO, i.e. at the level of equations of motion. It also contains the recently discovered covariant forms of the higher spin extensions of SDYM and SDGR, as well as SDYM and SDGR themselves. From the mathematical viewpoint the result is equivalent to taking the minimal model (in the sense of $L_{\infty }$-algebras) of the jet-space extension of the BV-BRST formulation of Chiral Higher Spin Gravity, thereby, containing also information about (presymplectic AKSZ) action, counterterms, anomalies, etc.

21 + Appendices + Refs = 34 pages; some typos fixed and comments added

References in corpus (21)

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• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Light-Front Higher-Spin Theories in Flat Space
• Effective action in a higher-spin background
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Chiral Higher Spin Theories and Self-Duality
• Partition function of free conformal higher spin theory
• Actions for Self-dual Higher Spin Gravities
• On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
• A Derivation of AdS/CFT for Vector Models
• First order parent formulation for generic gauge field theories
• One-loop Finiteness of Chiral Higher Spin Gravity
• Celestial $w_{1+\infty }$ Symmetries from Twistor Space
• Parent formulations, frame-like Lagrangians, and generalized auxiliary fields
• Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation Procedure
• Formal Higher Spin Gravities
• Twistor Constructions for Higher-spin Extensions of (Self-dual) Yang-Mills
• Flat Self-dual Gravity
• Characteristic Cohomology and Observables in Higher Spin Gravity
• Slightly Broken Higher Spin Symmetry: General Structure of Correlators
• Higher Spin Gravities and Presymplectic AKSZ Models

Cited by in corpus (11)

• Celestial chiral algebras, colour-kinematics duality and integrability
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• Chiral approach to massive higher spins
• Higher-Spin Self-Dual Yang-Mills and Gravity from the twistor space
• Minimal model of Chiral Higher Spin Gravity
• Chiral Higher Spin Gravity and Convex Geometry
• Towards higher-spin holography in flat space
• Chiral higher-spin holography in flat space: the Flato-Fronsdal theorem and lower-point functions
• On (spinor)-helicity and bosonization in $Ad{S}_4/CF{T}_3$
• Massless chiral fields in six dimensions
• Invariant traces of the flat space chiral higher-spin algebra as scattering amplitudes