On holomorphic sector of higher-spin theory

Abstract

Recent investigation of locality problem for higher-spin fields led to a vertex reconstruction procedure that involved elements of contraction of the original Vasiliev interaction algebra. Inspired by these results we propose the Vasiliev-like generating equations for holomorphic higher-spin interactions in four dimensions based on the observed contracted algebra. We specify the functional class that admits evolution on the proposed equations and brings in a systematic procedure of extracting all-order holomorphic vertices. A simple consequence of the proposed equations is space-time locality of the gauge field sector. We also show that vertices come with a remarkable shift symmetry.

arXiv comment37 pages. Few typos fixed. A major simplification of the projector identity resulted in the new form of eq. (4.11). Appendix B is extended correspondingly

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• Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields
• Scalar Electrodynamics and Higgs Mechanism in the Unfolded Dynamics Approach
• Gauge Invariant Lagrangian Formulations for Mixed Symmetry Higher Spin Bosonic Fields in AdS Spaces
• Unfolded Formulation of 4d Yang-Mills Theory
• Four-point functions and contact terms from higher-spin Ward identities of Chern-Simons-matter theory