Courant Algebroid Connections and String Effective Actions

TL;DR

This paper explores how connections on Courant algebroids can be used to geometrically describe string theory's low energy effective equations, providing new insights and examples like symplectic gravity and heterotic reduction.

Contribution

It introduces a class of Courant algebroid connections with properties analogous to Levi-Civita connections, linking them to string theory equations of motion.

Findings

Connections on Courant algebroids can encode string theory equations

Examples include symplectic gravity and heterotic reduction

Provides a detailed, self-contained mathematical framework

Abstract

Courant algebroids are a natural generalization of quadratic Lie algebras, appearing in various contexts in mathematical physics. A connection on a Courant algebroid gives an analogue of a covariant derivative compatible with a given fiber-wise metric. Imposing further conditions resembling standard Levi-Civita connections, one obtains a class of connections whose curvature tensor in certain cases gives a new geometrical description of equations of motion of low energy effective action of string theory. Two examples are given. One is the so called symplectic gravity, the second one is an application to the the so called heterotic reduction. All necessary definitions, propositions and theorems are given in a detailed and self-contained way.