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A_infty Algebras from Slightly Broken Higher Spin Symmetries

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Skvortsov,  Evgeny
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1809.10027.pdf
(Preprint), 486KB

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Citation

Sharapov, A., & Skvortsov, E. (in preparation). A_infty Algebras from Slightly Broken Higher Spin Symmetries.


Cite as: http://hdl.handle.net/21.11116/0000-0002-575E-4
Abstract
We define a class of $A_\infty$-algebras that are obtained by deformations of higher spin symmetries. While higher spin symmetries of a free CFT form an associative algebra, the slightly broken higher spin symmetries give rise to a minimal $A_\infty$-algebra extending the associative one. These $A_\infty$-algebras are related to non-commutative deformation quantization much as the unbroken higher spin symmetries result from the conventional deformation quantization. In the case of three dimensions there is an additional parameter that the $A_\infty$-structure depends on, which is to be related to the Chern-Simons level. The deformations corresponding to the bosonic and fermionic matter lead to the same $A_\infty$-algebra, thus manifesting the three-dimensional bosonization conjecture. In all other cases we consider, the $A_\infty$-deformation is determined by a generalized free field in one dimension lower.