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arXiv · 1712.03980

Homogeneous Nonrelativistic Geometries as Coset Spaces

Kevin T. Grosvenor·Jelle Hartong·Cynthia Keeler·Niels A. Obers
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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 Inönü-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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Kevin T. Grosvenor, Jelle Hartong, Cynthia Keeler, Niels A. Obers. 2018-08-07. Homogeneous Nonrelativistic Geometries as Coset Spaces. https://doi.org/10.1088/1361-6382%2Faad0f9

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