Non-geometric fluxes, quasi-Hopf twist deformations, and nonassociative quantum mechanics

Journal Article · Mon Dec 15 04:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4902378· OSTI ID:22403070

Mylonas, Dionysios; Schupp, Peter ^[1]

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1. Jacobs University Bremen, 28759 Bremen (Germany)

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.

• OSTI ID: 22403070
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 55; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
COMMUTATION RELATIONS
DEFORMATION
DUALITY
EXPECTATION VALUE
GEOMETRY
LIE GROUPS
PHASE SPACE
QUANTIZATION
QUANTUM MECHANICS