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Mathematische Annalen

, Volume 369, Issue 1–2, pp 539–595 | Cite as

Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry

  • Mario Garcia-FernandezEmail author
  • Roberto Rubio
  • Carl Tipler
Article

Abstract

We construct the space of infinitesimal variations for the Strominger system and an obstruction space to integrability, using elliptic operator theory. We initiate the study of the geometry of the moduli space, describing the infinitesimal structure of a natural foliation on this space. The associated leaves are related to generalized geometry and correspond to moduli spaces of solutions of suitable Killing spinor equations on a Courant algebroid. As an application, we propose a unifying framework for metrics with holonomy \(\mathrm {SU}(3)\) and solutions of the Strominger system.

Mathematics Subject Classification

58D27 53D18 

Notes

Acknowledgments

We thank Luis Álvarez-Cónsul, Bjorn Andreas, Vestislav Apostolov, Henrique Bursztyn, Ryushi Goto, Marco Gualtieri, Nigel Hitchin, Laurent Meersseman, Xenia de la Ossa, Dan Popovici, Brent Pym and Eirik Svanes for useful discussions. Part of this work was undertaken while CT was visiting IMPA, UFRJ, CRM, during visits of MGF and CT to CIRGET, and of RR to EPFL and ICMAT. We would like to thank these very welcoming institutions for providing a nice and stimulating working environment.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Mario Garcia-Fernandez
    • 1
    Email author
  • Roberto Rubio
    • 2
  • Carl Tipler
    • 3
  1. 1.Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM)MadridSpain
  2. 2.Instituto Nacional de Matemática Pura e Aplicada (IMPA)Rio de JaneiroBrazil
  3. 3.Département de MathématiquesLMBA, UMR CNRS 6205, Université de Bretagne OccidentaleBrest Cedex 3France

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