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

Dionysios Mylonas, Peter Schupp, Richard J. Szabo

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41 Citations (Scopus)
37 Downloads (Pure)

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 languageEnglish
Article number1.4902378
JournalJournal of Mathematical Physics
Volume55
Issue number12
Early online date3 Dec 2014
DOIs
Publication statusPublished - 2014

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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