Working with Nonassociative Geometry and Field Theory
arXiv:1601.07353
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.
20 pages; v2: Reference added; Contribution to the proceedings of the Corfu Summer Institute on Elementary Particle Physics and Gravity, September 1-26, 2015, Corfu, Greece; Final version published in Proceedings of Science
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