University of Hertfordshire

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Heterotic backgrounds via generalised geometry: moment maps and moduli

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Original languageEnglish
Article number71
Number of pages46
JournalJournal of High Energy Physics
Publication statusPublished - 16 Nov 2020


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 K\"ahler 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.


© 2020 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0:, which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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