Nonassociative differential geometry and gravity

Abstract

In this short contribution we introduce a nonassocaitive deformation of differential geometry and General Relativity. The nonassociativity is based on the string theory nongeometric R-flux. We use the twist formalism to consistently deform the algebra of infinitesimal diffeomorphisms into the quasi Hopf algebra of (deformed) infnitesimal diffeomorphisms and introduce the NA deformation of differential geometry. In particualr, we define the Levi-Civita connection, curvature tensor and torsion. The space-time quantities (curvature, torsion) are obtained by the zero momenum leaf projection to the space-time. The vacuum Einstein equation in space-time, expanded up to first order in the deformation parameter κ~ is obtained.