Higher Spin Gravities and Presymplectic AKSZ Models

TL;DR

This paper develops a presymplectic AKSZ sigma-model for 4D Higher Spin Gravity, aligning with AdS/CFT duality, and demonstrates its correctness in reproducing quantum commutators and symmetry algebra.

Contribution

It constructs a unique presymplectic AKSZ model for 4D Higher Spin Gravity that incorporates duality-consistent couplings and passes interaction consistency checks.

Findings

Correct quantum commutator structure derived

Algebra of higher spin symmetry currents obtained

Model depends on two coupling constants, consistent with duality

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.