2013/12/31 by Dionysios Mylonas, Peter Schupp, Richard J. Szabo · 1 citation
Mathematics · Physics and Astronomy · #hep-th #math-ph #math.MP #math.QA #quant-ph
paper · pdf · doi:10.1063/1.4902378
38 pages; v2: typos corrected, reference added; v3: typos corrected, comments about cyclicity added in section 4.2, references updated; Final version to be published in Journal of Mathematical Physics
arxiv created 2014/10/24 · arxiv updated 2015/06/18
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.