Nonassociative differential geometry and gravity with non-geometric fluxes

Abstract

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.

50 pages; v2: corrected comparison of curvature to ref. [14]; v3: clarifying comments added; Final version to be published in JHEP

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Cited by in corpus (22)

• Non-geometric backgrounds in string theory
• Double Field Theory and Membrane Sigma-Models
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• Braided Symmetries in Noncommutative Field Theory
• Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality
• $L_{\infty }$-Algebras of Einstein-Cartan-Palatini Gravity
• Footprint of spatial noncommutativity in resonant detectors of gravitational wave
• Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity
• Noncommutative gravity with self-dual variables
• Global Double Field Theory is Higher Kaluza-Klein Theory
• Nonassociative black holes in R-flux deformed phase spaces and relativistic models of G. Perelman thermodynamics
• Decoupling and integrability of nonassociative vacuum phase space gravitational equations with star and R-flux parametric deformations
• Nonassociative black ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks
• Nonassociative Ricci flows, star product and R-flux deformed black holes, and swampland conjectures
• Nonassociative gauge gravity theories with R-flux star products and Batalin-Vilkovisky quantization in algebraic quantum field theory
• Nonassociative geometry of nonholonomic phase spaces with star R-flux string deformations and (non) symmetric metrics
• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories
• Nonassicative cosmological solitonic R-flux deformations in gauge gravity and G. Perelman geometric flow thermodynamics
• Nonassociative Einstein-Dirac-Maxwell systems and R-flux modified Reissner-Nordström black holes and wormholes
• Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff-Sagnotti counter-terms, and geometric flows
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations
• Batalin-Fradkin-Vilkovisky quantization of Einstein gravity with off-diagonal solutions encoding Hořava type generating functions