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A_infty Algebras from Slightly Broken Higher Spin Symmetries

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

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1809.10027.pdf (Preprint), 486KB
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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: 2018-09-26
Publication Status: Not specified
Pages: 45 pages, some pictures
Publishing info: -
Rev. Method: -
Identifiers: arXiv: 1809.10027
URI: http://arxiv.org/abs/1809.10027
Degree: -

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