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Extended Riemannian Geometry I: Local Double Field Theory

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Abstract

We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds, and it yields extended notions of symmetries, dynamical data and constraints. In special cases, we recover general relativity with and without 1-, 2- and 3-form gauge potentials as well as DFT. We believe that our extended Riemannian geometry helps to clarify the role of various constructions in DFT. For example, it leads to a covariant form of the strong section condition. Furthermore, it should provide a useful step toward global and coordinate invariant descriptions of T- and U-duality invariant field theories.

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Acknowledgements

We would like to thank David Berman, Ralph Blumenhagen, André Coimbra, Dieter Lüst and Jim Stasheff for discussions. The work of CS was partially supported by the Consolidated Grant ST/L000334/1 from the UK Science and Technology Facilities Council. AD and CS want to thank the Department of Mathematics of Heriot-Watt University and the Institut für Theoretische Physik in Hannover for hospitality, respectively.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Appelstr. 2, 30167, Hannover, Germany

    Andreas Deser

  2. Istituto Nationale di Fisica Nucleare, Via P. Giuria 1, 10125, Turin, Italy

    Andreas Deser

  3. Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh, EH14 4AS, UK

    Christian Sämann

  4. Maxwell Institute for Mathematical Sciences, Edinburgh, UK

    Christian Sämann

  5. Higgs Centre for Theoretical Physics, Edinburgh, UK

    Christian Sämann

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  1. Andreas Deser
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Correspondence to Andreas Deser.

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Communicated by Boris Pioline.

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Deser, A., Sämann, C. Extended Riemannian Geometry I: Local Double Field Theory. Ann. Henri Poincaré 19, 2297–2346 (2018). https://doi.org/10.1007/s00023-018-0694-2

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