Torsion-free generalized connections and Heterotic Supergravity

TL;DR

This paper explores torsion-free generalized connections in the context of generalized geometry and derives the equations of motion for heterotic supergravity, connecting advanced geometric concepts with string theory physics.

Contribution

It introduces a new framework for torsion-free generalized connections on non-exact Courant algebroids and applies it to derive heterotic supergravity equations.

Findings

Development of torsion-free generalized connections compatible with generalized metrics

Mathematical derivation of heterotic supergravity equations of motion

Extension of generalized geometry to non-exact Courant algebroids

Abstract

This work revisits the notions of connection and curvature in generalized geometry, with emphasis on torsion-free generalized connections on a transitive Courant algebroid, compatible with a generalized metric. Non-exact Courant algebroids have been considered recently by R. Rubio in the context of $B_n$-generalised geometry and arise naturally from the theory of generalized reduction of Burzstyn, Cavalcanti and Gualtieri. As an application, we provide a mathematical derivation of the equations of motion of heterotic supergravity, inspired by the work of Coimbra, Strickland-Constable and Waldram.