2017/10/31 by Paolo Aschieri, Marija Dimitrijević Ćirić, Marija Dimitrijevic Ciric +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Connection (principal bundle) #Differential form #Differential geometry #Einstein #Formalism (music) #Geometric Analysis and Curvature Flows #Metric (unit) #Ricci curvature #Riemannian geometry #String field theory #String theory #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.1007/jhep02(2018)036
50 pages; v2: corrected comparison of curvature to ref. [14]; v3: clarifying comments added; Final version to be published in JHEP
openalex created_date 2017/11/10 · arxiv created 2018/01/30 · openalex publication_date 2018/02/01 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/05
We systematically develop the metric aspects of nonassociative differential geometry tailored to the parabolic phase space model of constant locally non-geometric closed string vacua, and use it to construct preliminary steps towards a nonassociative theory of gravity on spacetime. We obtain explicit expressions for the torsion, curvature, Ricci tensor and Levi-Civita connection in nonassociative Riemannian geometry on phase space, and write down Einstein field equations. We apply this formalism to construct R-flux corrections to the Ricci tensor on spacetime, and comment on the potential implications of these structures in non-geometric string theory and double field theory.