Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher Quantum Geometry and Non-Geometric String Theory   We present a concise overview of the physical and mathematical structures
underpinning the appearence of nonassociative deformations of geometry in
non-geometric string theory. Starting from a quick recap of the appearence of
noncommutative product and commutator deformations of geometry in open string
theory with $B$-fields, we argue on physical principles that closed strings
should instead probe triproduct and tribracket deformations in backgrounds of
locally non-geometric fluxes. After describing the toy model of electric
charges moving in fields of smooth distributions of magnetic charge as a
physical introduction to the notions of nonassociative geometry, we review the
description of non-geometric fluxes in generalized geometry and double field
theory, and the worldsheet calculations suggesting the appearence of
nonassociative deformations, together with their caveats. We discuss how
algebroids and their associated AKSZ sigma-models give a description of
non-geometric backgrounds in terms of higher geometry, and consider the
quantization of the membrane sigma-model which geometrizes closed strings with
$R$-flux. From this we derive an explicit nonassociative star product for the
quantum geometry of the closed string phase space, and apply it to derive the
triproducts that appear in conformal field theory correlation functions, to
describe a consistent treatment of nonassociative quantum mechanics, to
demonstrate quantitatively the coarse-graining of spacetime due to $R$-flux,
and to describe the quantization of Nambu brackets. We also briefly review how
these constructions lead to a nonassociative theory of gravity, their uplifts
to non-geometric M-theory, and the role played by $L_\infty$-algebras in these
developments.

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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio