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A∞ algebras from slightly broken higher spin symmetries

Sharapov, A., & Skvortsov, E. (2019). A∞ algebras from slightly broken higher spin symmetries. Journal of High Energy Physics, 2019(9): 24. doi:10.1007/JHEP09(2019)024.

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Creators:
Sharapov, Alexey, Author
Skvortsov, Evgeny1, Author
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014

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Free keywords: High Energy Physics - Theory, hep-th
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.

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Dates: 2018-09-262019
Publication Status: Published in print
Pages: 45 pages, some pictures
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Identifiers: arXiv: 1809.10027
URI: http://arxiv.org/abs/1809.10027
DOI: 10.1007/JHEP09(2019)024
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Title: Journal of High Energy Physics
Source Genre: Journal
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Pages: - Volume / Issue: 2019 (9) Sequence Number: 24 Start / End Page: - Identifier: -