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.

arXiv comment21 + Appendices + Refs = 34 pages; some typos fixed and comments added

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• 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