Torsional Newton–Cartan geometry and the Schrödinger algebra

@article{Bergshoeff2014TorsionalNG,
  title={Torsional Newton–Cartan geometry and the Schr{\"o}dinger algebra},
  author={Eric Bergshoeff and Jelle Hartong and Jan Rosseel},
  journal={Classical and Quantum Gravity},
  year={2014},
  volume={32},
  pages={135017}
}
We show that by gauging the Schrodinger algebra with critical exponent z and imposing suitable curvature constraints, that make diffeomorphisms equivalent to time and space translations, one obtains a geometric structure known as (twistless) torsional Newton-Cartan geometry (TTNC). This is a version of torsional Newton-Cartan geometry (TNC) in which the timelike vielbein t mu must be hypersurface orthogonal. For z = 2 this version of TTNC geometry is very closely related to the one appearing in… Expand

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References

SHOWING 1-10 OF 58 REFERENCES
Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography
A bstractFor a specific action supporting z = 2 Lifshitz geometries we identify the Lifshitz UV completion by solving for the most general solution near the Lifshitz boundary. We identify all theExpand
Torsional Newton-Cartan geometry and Lifshitz holography
We obtain the Lifshitz UV completion in a specific model for z=2 Lifshitz geometries. We use a vielbein formalism which enables identification of all the sources as leading components of well-chosenExpand
Null-Killing vector dimensional reduction and Galilean geometrodynamics
The solutions of Einstein's equations admitting one non-null Killing vector field are best studied with the projection formalism of Geroch. When the Killing vector is lightlike, the projection ontoExpand
Newtonian gravity and the Bargmann algebra
We show how the Newton-Cartan formulation of Newtonian gravity can be obtained from gauging the Bargmann algebra, i.e., the centrally extended Galilean algebra. In this gauging procedure severalExpand
Non-relativistic conformal symmetries and Newton–Cartan structures
This paper provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton–Cartan spacetime. The Lie algebras of non-relativistic conformalExpand
Schrödinger Invariance from Lifshitz Isometries in Holography and Field Theory
We study non-relativistic field theory coupled to a torsional Newton-Cartan geometry both directly as well as holographically. The latter involves gravity on asymptotically locally LifshitzExpand
Conformal Lifshitz gravity from holography
A bstractWe show that holographic renormalization of relativistic gravity in asymptotically Lifshitz spacetimes naturally reproduces the structure of gravity with anisotropic scaling: the holographicExpand
Lifshitz holography: the whole shebang
A bstractWe provide a general algorithm for constructing the holographic dictionary for any asymptotically locally Lifshitz background, with or without hyperscaling violation, and for any values ofExpand
3D Newton?Cartan supergravity
We construct a supersymmetric extension of three-dimensional Newton–Cartan gravity by gauging a super-Bargmann algebra. In order to obtain a non-trivial supersymmetric extension of the BargmannExpand
Holographic renormalization for z = 2 Lifshitz spacetimes from AdS
Lifshitz spacetimes with the critical exponent z = 2 can be obtained by the dimensional reduction of Schrodinger spacetimes with the critical exponent z = 0. The latter spacetimes are asymptoticallyExpand
...
1
2
3
4
5
...