Heterotic Reduction of Courant Algebroid Connections and Einstein-Hilbert Actions

TL;DR

This paper explores Levi-Civita connections on Courant algebroids, generalizes curvature tensors, and derives scalar curvatures leading to Einstein-Hilbert actions relevant in supergravity, with a focus on reduction processes.

Contribution

It introduces a generalized framework for curvature and scalar curvature on Courant algebroids, including the heterotic case, and analyzes their reduction for supergravity applications.

Findings

Derived generalized scalar curvatures for Courant algebroids

Established reduction procedures for metrics and connections

Connected curvature concepts to Einstein-Hilbert actions in supergravity

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.