Homogeneous nonrelativistic geometries as coset spaces

Kevin T. Grosvenor, Jelle Hartong, Cynthia Keeler, Niels A. Obers

Research output: Contribution to journalArticle

8 Citations (Scopus)

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.

Original languageEnglish (US)
Article number175007
JournalClassical and Quantum Gravity
Volume35
Issue number17
DOIs
StatePublished - Jul 27 2018

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newton
algebra
geometry
tangents
string theory
contraction
gravitation
symmetry

Keywords

  • Bargmann algebra
  • coset space
  • Newton-Cartan geometry
  • Newton-Hooke algebra
  • Schrodinger algebra

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

Homogeneous nonrelativistic geometries as coset spaces. / Grosvenor, Kevin T.; Hartong, Jelle; Keeler, Cynthia; Obers, Niels A.

In: Classical and Quantum Gravity, Vol. 35, No. 17, 175007, 27.07.2018.

Research output: Contribution to journalArticle

Grosvenor, Kevin T. ; Hartong, Jelle ; Keeler, Cynthia ; Obers, Niels A. / Homogeneous nonrelativistic geometries as coset spaces. In: Classical and Quantum Gravity. 2018 ; Vol. 35, No. 17.
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