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A Geometric Construction of Solutions to 11D Supergravity

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Abstract

Necessary and sufficient conditions are provided for a class of warped product manifolds with non-vanishing flux to be supersymmetric solutions of 11D supergravity. Many non-compact, but complete solutions can be obtained in this manner, including the multi-membrane solution initially found by Duff and Stelle. In a different direction, an explicit 5-parameter moduli space of solutions to 11D supergravity is also constructed which can be viewed as non-supersymmetric deformations of the Duff–Stelle solution.

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Acknowledgements

We would like to thank David Andriot, Michael Duff, and Daniël Prins for bringing some important references to our attention. We also thank the anonymous referees for making the exposition more readable.

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Authors and Affiliations

  1. Department of Mathematics, Columbia University, New York, NY, 10027, USA

    Teng Fei, Bin Guo & Duong H. Phong

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  1. Teng Fei
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  2. Bin Guo
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  3. Duong H. Phong
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Correspondence to Teng Fei.

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Communicated by N. Nekrasov

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Work supported in part by National Science Foundation Grants DMS-12-66033 and DMS-17-10500.

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Fei, T., Guo, B. & Phong, D.H. A Geometric Construction of Solutions to 11D Supergravity. Commun. Math. Phys. 369, 811–836 (2019). https://doi.org/10.1007/s00220-019-03322-w

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