$\mathbf{O}(D,D)$ completion of the Einstein Field Equations

Abstract

Upon treating the whole closed-string massless NS-NS sector as stringy graviton fields, Double Field Theory may evolve into `Stringy Gravity'. In terms of an $\mathbf{O}(D,D)$ covariant differential geometry beyond Riemann, we present the definitions of the off-shell conserved stringy Einstein curvature tensor and the on-shell conserved stringy Energy-Momentum tensor. Equating them, all the equations of motion of the massless sector are unified into a single expression, $G_{AB}=8\pi G{T}_{AB}$, carrying $\mathbf{O}(D,D)$ vector indices, which we dub `the Einstein Double Field Equations'.

1+11 pages, contribution to the proceedings of the workshop "Dualities and Generalized Geometries", Corfu Summer Institute 2018

References in corpus (8)

• Differential geometry with a projection: Application to double field theory
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• The Exceptional Sigma Model
• Kaluza-Klein reduction on a maximally non-Riemannian space is moduli-free
• Type II strings are Exceptional
• Stringy Gravity: Solving the Dark Problems at `short' distance

Cited by in corpus (3)

• String Theory and non-Riemannian Geometry
• Non-Riemannian gravity actions from double field theory
• $\mathbf{O}(D,D)$ completion of the Friedmann equations