2015/04/15 by Paolo Aschieri, Richard J. Szabo
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Computer science #Configuration space #Differential (mechanical device) #Differential form #Differential geometry #Geometry #Mathematical analysis #Mathematics #Noncommutative and Quantum Gravity Theories #Phase space #Physics #Quantum mechanics #Space (punctuation) #Star (game theory) #String (physics) #String theory #Theoretical physics #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.1088/1742-6596/634/1/012004
33 pages; Contribution to the Proceedings of "Conceptual and Technical Challenges for Quantum Gravity", September 8-12, 2014, Sapienza University of Rome, Italy; to be published in Journal of Physics Conference Series, eds. G. Amelino-Camelia, P. Martinetti and J.-C. Wallet
arxiv created 2015/04/15 · openalex publication_date 2015/08/03 · arxiv updated 2015/09/02 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
We elucidate relations between different approaches to describing the nonassociative deformations of geometry that arise in non-geometric string theory. We demonstrate how to derive configuration space triproducts exactly from nonassociative phase space star products and extend the relationship in various directions. By foliating phase space with leaves of constant momentum we obtain families of Moyal-Weyl type deformations of triproducts, and we generalize them to new triproducts of differential forms and of tensor fields. We prove that nonassociativity disappears on-shell in all instances. We also extend our considerations to the differential geometry of nonassociative phase space, and study the induced deformations of configuration space diffeomorphisms. We further develop general prescriptions for deforming configuration space geometry from the nonassociative geometry of phase space, thus paving the way to a nonassociative theory of gravity in non-geometric flux compactifications of string theory.