2014/02/28 by Dionysios Mylonas, Peter Schupp, Mylonas, Dionysios +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1402.7306
openalex publication_date 2014/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe nonassociative deformations of geometry probed by closed strings\nin non-geometric flux compactifications of string theory. We show that these\nnon-geometric backgrounds can be geometrised through the dynamics of open\nmembranes whose boundaries propagate in the phase space of the target space\ncompactification, equiped with a twisted Poisson structure. The effective\nmembrane target space is determined by the standard Courant algebroid over the\ntarget space twisted by an abelian gerbe in momentum space. Quantization of the\nmembrane sigma-model leads to a proper quantization of the non-geometric\nbackground, which we relate to Kontsevich's formalism of global deformation\nquantization that constructs a noncommutative nonassociative star product on\nphase space. We construct Seiberg-Witten type maps between associative and\nnonassociative backgrounds, and show how they may realise a nonassociative\ndeformation of gravity. We also explain how this approach is related to the\nquantization of certain Lie 2-algebras canonically associated to the twisted\nCourant algebroid, and cochain twist quantization using suitable quasi-Hopf\nalgebras of symmetries in the phase space description of R-space which\nconstructs a Drinfel'd twist with non-trivial 3-cocycle. We illustrate and\napply our formalism to present a consistent phase space formulation of\nnonassociative quantum mechanics.\n