期刊
CLASSICAL AND QUANTUM GRAVITY
卷 35, 期 17, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1361-6382/aad0f9
关键词
coset space; Newton-Cartan geometry; Bargmann algebra; Newton-Hooke algebra; Schrodinger algebra
类别
资金
- Simons Center for Geometry and Physics, Stony Brook University
- ERC [291092]
- STSM Grant from COST Action [MP1405]
- European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie [656900]
- Independent Research Fund Denmark [DFF-6108-00340]
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 cosecs via Intinii-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.
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