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An action for extended string Newton-Cartan gravity

A preprint version of the article is available at arXiv.

Abstract

We construct an action for four-dimensional extended string Newton-Cartan gravity which is an extension of the string Newton-Cartan gravity that underlies nonrelativistic string theory. The action can be obtained as a nonrelativistic limit of the EinsteinHilbert action in General Relativity augmented with a term that contains an auxiliary two-form and one-form gauge field that both have zero flux on-shell. The four-dimensional extended string Newton-Cartan gravity is based on a central extension of the algebra that underlies string Newton-Cartan gravity.

The construction is similar to the earlier construction of a three-dimensional Chern-Simons action for extended Newton-Cartan gravity, which is based on a central extension of the algebra that underlies Newton-Cartan gravity. We show that this three-dimensional action is naturally obtained from the four-dimensional action by a reduction over the spatial isometry direction longitudinal to the string followed by a truncation of the extended string Newton-Cartan gravity fields. Our construction can be seen as a special case of the construction of an action for extended p-brane Newton-Cartan gravity in p + 3 dimensions.

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Correspondence to Eric A. Bergshoeff.

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ArXiv ePrint: 1810.09387

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Bergshoeff, E.A., Grosvenor, K.T., Şimşek, C. et al. An action for extended string Newton-Cartan gravity. J. High Energ. Phys. 2019, 178 (2019). https://doi.org/10.1007/JHEP01(2019)178

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  • DOI: https://doi.org/10.1007/JHEP01(2019)178

Keywords

  • Bosonic Strings
  • Classical Theories of Gravity