Torsion-free generalized connections and Heterotic Supergravity

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.

27 pages. Introduction modified and new references. Added Remark 3.8 about the Levi-Civita connection in generalized geometry

References in corpus (9)

• Generalised Geometry for M-Theory
• Differential geometry with a projection: Application to double field theory
• Generalized complex geometry
• Torsional Heterotic Geometries
• Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic Compactifications
• Algebroids, Heterotic Moduli Spaces and the Strominger System
• Non-Kaehler Heterotic String Compactifications with non-zero fluxes and constant dilaton
• Comments on Heterotic Flux Compactifications
• Generalized geometry, T-duality, and renormalization group flow

Cited by in corpus (60)

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• Heterotic Effective Action and Duality Symmetries Revisited
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• Green-Schwarz mechanism and ${\alpha }^{\prime }$-deformed Courant brackets
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• Hitchhiker's Guide to Courant Algebroid Relations
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• Kaluza-Klein Reduction of Low-Energy Effective Actions: Geometrical Approach
• Graded Generalized Geometry
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• Effective Actions for $\sigma$-Models of Poisson-Lie Type
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• Supergravity Fluxes and Generalised Geometry
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• Heterotic solitons on four-manifolds