Abstract
We analyse the symmetries underlying nonassociative deformations of geometry in nongeometric Rflux compactifications which arise via Tduality from closed strings with constant geometric fluxes. Starting from the nonabelian Lie algebra of translations and Bopp shifts in phase space, together with a suitable cochain twist, we construct the quasiHopf algebra of symmetries that deforms the algebra of functions and the exterior differential calculus in the phase space description of nonassociative Rspace. In this setting, nonassociativity is characterised by the associator 3cocycle which controls noncoassociativity of the quasiHopf algebra. We use abelian 2cocycle 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 2cyclicity and 3cyclicity. Using this star product quantization on phase space together with 3cyclicity, we formulate a consistent version of nonassociative quantum mechanics, in which we calculate the expectation values of area and volume operators, and find coarsegraining of the string background due to the Rflux.
Original language  English 

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
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Richard Joseph Szabo
 School of Mathematical & Computer Sciences  Professor
 School of Mathematical & Computer Sciences, Mathematics  Professor
Person: Academic (Research & Teaching)