Heterotic Reduction of Courant Algebroid Connections and Einstein-Hilbert Actions

Abstract

We discuss Levi-Civita connections on Courant algebroids. We define an appropriate generalization of the curvature tensor and compute the corresponding scalar curvatures in the exact and heterotic case, leading to generalized (bosonic) Einstein-Hilbert type of actions known from supergravity. In particular, we carefully analyze the process of the reduction for the generalized metric, connection, curvature tensor and the scalar curvature.

New section and several references added based on the journal review

References in corpus (13)

• Double Field Theory
• Differential geometry with a projection: Application to double field theory
• T-duality and ${\alpha }^{\prime }$-corrections
• Double Field Theory at Order ${\alpha }^{\prime }$
• Frame-like Geometry of Double Field Theory
• Heterotic $\alpha$'-corrections in Double Field Theory
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• Green-Schwarz mechanism and ${\alpha }^{\prime }$-deformed Courant brackets
• Double Metric, Generalized Metric and ${\alpha }^{\prime }$-Geometry
• Leibniz algebroids, generalized Bismut connections and Einstein-Hilbert actions
• Gravity theory on Poisson manifold with $R$-flux
• The first Pontryagin class
• Transitive Courant algebroids

Cited by in corpus (8)

• Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle
• Extended Riemannian Geometry II: Local Heterotic Double Field Theory
• Contravariant Gravity on Poisson Manifolds and Einstein Gravity
• Kaluza-Klein Reduction of Low-Energy Effective Actions: Geometrical Approach
• Graded Generalized Geometry
• Effective Actions for $\sigma$-Models of Poisson-Lie Type
• A gravitational action with stringy $Q$ and $R$ fluxes via deformed differential graded Poisson algebras
• The standard cohomology of regular Courant algebroids