Journal of High Energy Physics

, 2019:178 | Cite as

An action for extended string Newton-Cartan gravity

  • Eric A. BergshoeffEmail author
  • Kevin T. Grosvenor
  • Ceyda Şimşek
  • Ziqi Yan
Open Access
Regular Article - Theoretical Physics


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.


Bosonic Strings Classical Theories of Gravity 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Eric A. Bergshoeff
    • 1
    Email author
  • Kevin T. Grosvenor
    • 2
  • Ceyda Şimşek
    • 1
  • Ziqi Yan
    • 3
  1. 1.Van Swinderen InstituteUniversity of GroningenGroningenThe Netherlands
  2. 2.Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität WürzburgWürzburgGermany
  3. 3.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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