Abstract
We define a class of A∞-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∞-algebra extending the associative one. These A∞-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∞-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∞-algebra, thus manifesting the three-dimensional bosonization conjecture. In all other cases we consider, the A∞-deformation is determined by a generalized free field in one dimension lower.
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Sharapov, A., Skvortsov, E. A∞ algebras from slightly broken higher spin symmetries. J. High Energ. Phys. 2019, 24 (2019). https://doi.org/10.1007/JHEP09(2019)024
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DOI: https://doi.org/10.1007/JHEP09(2019)024