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

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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.

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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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Authors and Affiliations

  1. Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Nicolás Cabrera 13–15, Cantoblanco, 28049, Madrid, Spain

    Mario Garcia-Fernandez

  2. Instituto Nacional de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, RJ, 22460-320, Brazil

    Roberto Rubio

  3. Département de Mathématiques, LMBA, UMR CNRS 6205, Université de Bretagne Occidentale, 6, Avenue Victor Le Gorgeu, 29238, Brest Cedex 3, France

    Carl Tipler

Authors
  1. Mario Garcia-Fernandez
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  2. Roberto Rubio
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Corresponding author

Correspondence to Mario Garcia-Fernandez.

Additional information

Communicated by Ngaiming Mok.

This Project has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No. 655162. This work is partially supported by an ESF—Short Visit Grant 5717 within the framework of the ITGP network. MGF is supported by a Marie Sklodowska-Curie Grant and was initially supported by ICMAT Severo Ochoa Project SEV-2011-0087 and by the École Polytechnique Fédéral de Lausanne. RR is supported by IMPA and was initially supported by QGM through its partnership with the Mathematical Institute of Oxford. CT is partially supported by Agence Nationale de la Recherche—ANR Project EMARKS.

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Garcia-Fernandez, M., Rubio, R. & Tipler, C. Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry. Math. Ann. 369, 539–595 (2017). https://doi.org/10.1007/s00208-016-1463-5

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  • DOI: https://doi.org/10.1007/s00208-016-1463-5

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