Nonassociative differential geometry and gravity with non-geometric fluxes

TL;DR

This paper develops a nonassociative differential geometry framework for string theory's non-geometric flux backgrounds, deriving geometric quantities and Einstein equations to explore gravity modifications.

Contribution

It introduces explicit formulas for torsion, curvature, and Ricci tensor in nonassociative geometry, and formulates Einstein equations in this novel setting.

Findings

Derived nonassociative torsion and curvature expressions.

Constructed nonassociative Einstein field equations.

Analyzed R-flux corrections to spacetime Ricci tensor.

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.