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.
Highlights
Quantization of Higher Spin Gravities (HSGRA) is an important open problem together with the problem of constructing more viable HSGRA
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
There is a number of immediate advantages of the presymplectic approach. Among these are (i) minimality: one does not have to introduce any auxiliary fields on top of what are already present in Eq (∗); (ii) background independence and gauge invariance: we do not have to pick any particular vacuum, like AdS4 and the gauge symmetry is fully taken into account to every order in the weak curvature expansion; (iii) relation to the canonical quantization and to the Lagrangian formulation that
Summary
Quantization of Higher Spin Gravities (HSGRA) is an important open problem together with the problem of constructing more viable HSGRA. We consider another approach to quantizing (non-)Lagrangian theories It employs the concept of a covariant presymplectic structure introduced in [56], [57]. There is a number of immediate advantages of the presymplectic approach Among these are (i) minimality: one does not have to introduce any auxiliary fields on top of what are already present in Eq (∗); (ii) background independence and gauge invariance: we do not have to pick any particular vacuum, like AdS4 and the gauge symmetry is fully taken into account to every order in the weak curvature expansion; (iii) relation to the canonical quantization and to the Lagrangian formulation that.
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