@article{83df34abf96147eb859d292ce0c375fc,
title = "Homogeneous nonrelativistic geometries as coset spaces",
abstract = "We generalize the coset procedure of homogeneous spacetimes in (pseudo-) Riemannian geometry to non-Lorentzian geometries. These are manifolds endowed with nowhere vanishing invertible vielbeins that transform under local non-Lorentzian tangent space transformations. In particular we focus on nonrelativistic symmetry algebras that give rise to (torsional) Newton-Cartan geometries, for which we demonstrate how the Newton-Cartan metric complex is determined by degenerate co- and contravariant symmetric bilinear forms on the coset. In specific cases we also show the connection of the resulting nonrelativistic coset spacetimes to pseudo-Riemannian cosets via Inonu-Wigner contraction of relativistic algebras as well as null reduction. Our construction is of use for example when considering limits of the AdS/CFT correspondence in which nonrelativistic spacetimes appear as gravitational backgrounds for nonrelativistic string or gravity theories.",
keywords = "Bargmann algebra, Newton-Cartan geometry, Newton-Hooke algebra, Schrodinger algebra, coset space",
author = "Grosvenor, {Kevin T.} and Jelle Hartong and Cynthia Keeler and Obers, {Niels A.}",
note = "Funding Information: Action MP1405 QSPACE. The work of CK was partially supported by the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie grant agreement No 656900. The work of NO is supported in part by the project {\textquoteleft}Towards a deeper understanding of black holes with nonrelativistic holography{\textquoteright} of the Independent Research Fund Denmark (grant number DFF-6108-00340). Funding Information: We would like to thank Eric Bergshoeff, Jaume Gomis, Diego Hofman, Yang Lei, Gerben Oling, Sakura Schafer-Nameki and Wei Song for useful discussions. The authors gratefully acknowledge support from the Simons Center for Geometry and Physics, Stony Brook University at which some of the research for this paper was performed during the 2017 workshop {\textquoteleft}Applied Newton–Cartan Geometry{\textquoteright}. JH acknowledges the hospitality of the Niels Bohr Institute. The work of KTG is supported by the ERC Advanced Grant 291092 {\textquoteleft}Exploring the Quantum Universe{\textquoteright}. The work of JH was in part supported by a STSM Grant from COST Publisher Copyright: {\textcopyright} 2018 IOP Publishing Ltd.",
year = "2018",
month = jul,
day = "27",
doi = "10.1088/1361-6382/aad0f9",
language = "English (US)",
volume = "35",
journal = "Classical and Quantum Gravity",
issn = "0264-9381",
publisher = "IOP Publishing Ltd.",
number = "17",
}