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||Proceedings of Science|
|Publication status||Published - 2016|
|Event||Corfu Summer Institute “School and Workshops on Elementary Particle Physics and Gravity” - Corfu, Greece|
Duration: 21 Sep 2015 → 27 Sep 2015