Higher Spin Gravities and Presymplectic AKSZ Models

Abstract

As a step towards quantization of Higher Spin Gravities we construct the presymplectic AKSZ sigma-model for $4d$ Higher Spin Gravity which is AdS/CFT dual of Chern-Simons vector models. It is shown that the presymplectic structure leads to the correct quantum commutator of higher spin fields and to the correct algebra of the global higher spin symmetry currents. The presymplectic AKSZ model is proved to be unique, it depends on two coupling constants in accordance with the AdS/CFT duality, and it passes some simple checks of interactions.

arXiv comment43+Appendices+biblio=70 pages; comments and refs added, matches the published version

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• Chiral approach to partially-massless fields
• Presymplectic gauge PDEs and Lagrangian BV formalism beyond jet-bundles
• Gauge Invariant Lagrangian Formulations for Mixed Symmetry Higher Spin Bosonic Fields in AdS Spaces
• Massless chiral fields in six dimensions