Heterotic backgrounds via generalised geometry: moment maps and moduli

Abstract

We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an $SU(3)\times Spin(6+n)$ structure within $O(6,6+n)\times {\mathbb{R}}^{+}$ generalised geometry. Supersymmetry of the background is encoded in the existence of an involutive subbundle of the generalised tangent bundle and the vanishing of a moment map for the action of diffeomorphisms and gauge symmetries. We give both the superpotential and the Kähler potential for a generic background, showing that the latter defines a natural Hitchin functional for heterotic geometries. Intriguingly, this formulation suggests new connections to geometric invariant theory and an extended notion of stability. Finally we show that the analysis of infinitesimal deformations of these geometric structures naturally reproduces the known cohomologies that count the massless moduli of supersymmetric heterotic backgrounds.

arXiv comment50 pages; references added

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Cited by in corpus (5)

• Heterotic Quantum Cohomology
• Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces
• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes
• Exceptional complex structures and the hypermultiplet moduli of 5d Minkowski compactifications of M-theory
• Balanced and Aeppli Parameters for the Heterotic Moduli