Working with Nonassociative Geometry and Field Theory

Gwendolyn Elizabeth Barnes, Alexander Schenkel, Richard Joseph Szabo

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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.
Original languageEnglish
JournalProceedings of Science
Publication statusPublished - 2016
EventCorfu Summer Institute 2015: School and Workshops on Elementary Particle Physics and Gravity - Corfu, Greece
Duration: 21 Sept 201527 Sept 2015


  • hep-th
  • math-ph
  • math.MP
  • math.QA


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