### Abstract

We analyse the symmetries underlying nonassociative deformations of geometry in non-geometric R-flux compactifications which arise via T-duality from closed strings with constant geometric fluxes. Starting from the non-abelian Lie algebra of translations and Bopp shifts in phase space, together with a suitable cochain twist, we construct the quasi-Hopf algebra of symmetries that deforms the algebra of functions and the exterior differential calculus in the phase space description of nonassociative R-space. In this setting, nonassociativity is characterised by the associator 3-cocycle which controls non-coassociativity of the quasi-Hopf algebra. We use abelian 2-cocycle twists to construct maps between the dynamical nonassociative star product and a family of associative star products parametrized by constant momentum surfaces in phase space. We define a suitable integration on these nonassociative spaces and find that the usual cyclicity of associative noncommutative deformations is replaced by weaker notions of 2-cyclicity and 3-cyclicity. Using this star product quantization on phase space together with 3-cyclicity, we formulate a consistent version of nonassociative quantum mechanics, in which we calculate the expectation values of area and volume operators, and find coarse-graining of the string background due to the R-flux.

Original language | English |
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Article number | 1.4902378 |

Journal | Journal of Mathematical Physics |

Volume | 55 |

Issue number | 12 |

Early online date | 3 Dec 2014 |

DOIs | |

Publication status | Published - 2014 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'Non-geometric fluxes, quasi-Hopf twist deformations, and nonassociative quantum mechanics'. Together they form a unique fingerprint.

## Profiles

## Richard Joseph Szabo

- School of Mathematical & Computer Sciences - Professor
- School of Mathematical & Computer Sciences, Mathematics - Professor

Person: Academic (Research & Teaching)

## Cite this

*Journal of Mathematical Physics*,

*55*(12), [1.4902378]. https://doi.org/10.1063/1.4902378