An action for extended string Newton-Cartan gravity

Bergshoeff, E. A., Grosvenor, K. T., Şimşek, C. & Yan, Z., 23-Jan-2019, In : Journal of High Energy Physics. 2019, 1, 21 p., 178.

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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.

Original languageEnglish
Article number178
Number of pages21
JournalJournal of High Energy Physics
Issue number1
Publication statusPublished - 23-Jan-2019


  • Bosonic Strings, Classical Theories of Gravity

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