An action for extended string Newton-Cartan gravity
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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.
KeywordsBosonic Strings Classical Theories of Gravity
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- E.A. Bergshoeff, J. Gomis, J. Rosseel, C. Şimşek and Z. Yan, work in progress.Google Scholar
- J.-M. Levy-Léblond, Galilei Group and Galilean Invariance, on Group Theory and its Applications, E.M. Loebl ed., Academic Press (2014) [DOI: https://doi.org/10.1016/B978-0-12-455152-7.50011-2].
- J.M. Izquierdo, Lie algebra expansions and three-dimensional Galilean supergravity, talk given at the Spanish-Portuguese Relativist Meeting (EREP) 2018, Palencia, Spain, September (2018).Google Scholar