Dirac structures on nilmanifolds and coexistence of fluxes

Abstract

We study some aspects of the generalized geometry of nilmanifolds and examine to which extent different types of fluxes can coexist on them. Nilmanifolds constitute a class of homogeneous spaces which are interesting in string compactifications with fluxes since they carry geometric flux by construction. They are generalized Calabi-Yau spaces and therefore simple examples of generalized geometry at work. We identify and classify Dirac structures on nilmanifolds, which are maximally isotropic subbundles closed under the Courant bracket. In the presence of non-vanishing fluxes, these structures are twisted and closed under appropriate extensions of the Courant bracket. Twisted Dirac structures on a nilmanifold may carry multiple coexistent fluxes of any type. We also show how dual Dirac structures combine to Courant algebroids and work out an explicit example where all types of generalized fluxes coexist. These results may be useful in the context of general flux compactifications in string theory.

1+25 pages; v2: clarifying comments and 6 references added, published version

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Cited by in corpus (9)

• NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes
• Double Field Theory and Membrane Sigma-Models
• Sigma models for genuinely non-geometric backgrounds
• Beyond the standard gauging: gauge symmetries of Dirac Sigma Models
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• Poisson-generalized geometry and $R$-flux
• Extended Riemannian Geometry III: Global Double Field Theory with Nilmanifolds
• Phase space quantization, noncommutativity and the gravitational field
• Pre-NQ Manifolds and Correspondence Spaces: the Nilmanifold Example