Working with Nonassociative Geometry and Field Theory

E. Barnes, Gwendolyn; Schenkel, Alexander; J. Szabo, Richard

Abstract

We review aspects of our formalism for differential geometry on noncommutative and nonassociative spaces which arise from cochain twist deformation quantization of manifolds. We work in the simplest setting of trivial vector bundles and flush out the details of our approach providing explicit expressions for all bimodule operations, and for connections and curvature. As applications, we describe the constructions of physically viable action functionals for Yang-Mills theory and Einstein-Cartan gravity on noncommutative and nonassociative spaces, as first steps towards more elaborate models relevant to non-geometric flux deformations of geometry in closed string theory.

• Journal Article Type: Article
• Conference Name: Corfu Summer Institute “School and Workshops on Elementary Particle Physics and Gravity”
• Acceptance Date: Nov 11, 2016
• Publication Date: Nov 11, 2016
• Deposit Date: Sep 11, 2019
• Publicly Available Date: Sep 24, 2019
• Journal: Proceedings of Science
• Publisher: Sissa Medialab
• Peer Reviewed: Peer Reviewed
• Volume: 263
• DOI: https://doi.org/10.22323/1.263.0081
• Keywords: High Energy Physics - Theory; Mathematical Physics; Quantum Algebra
• Public URL: https://nottingham-repository.worktribe.com/output/2460513
• Publisher URL: https://pos.sissa.it/263/081