Torsional Newton–Cartan geometry and the Schrödinger algebra
By Eric Bergshoeff, J. Hartong, Jan Rosseel. 2014
144 citations recorded by the source corpus.
We show that by gauging the Schrödinger 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 τ &mgr; ?> must be hypersurface orthogonal. For z = 2 this version of TTNC geometry is very closely related to the one appearing in holographic duals of z = 2 Lifshitz space-times based on Einstein gravity coupled to massive vector fields in the bulk. For z ≠ 2 ?> there is however an extra degree of freedom b0 that does not appear in the holographic setup. We show that the result of the gauging procedure can be extended to include a Stückelberg scalar χ that shifts under the particle number generator of the Schrödinger algebra, as well as an extra special conformal symmetry that allows one to gauge away b0. The resulting version of TTNC geometry is the one that appears in the holographic setup. This shows that Schrödinger symmetries play a crucial role in holography for Lifshitz space-times and that in fact the entire boundary geometry is dictated by local Schrödinger invariance. Finally we show how to extend the formalism to generic TNC geometries by relaxing the hypersurface orthogonality condition for the timelike vielbein τ &mgr; ?> .
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/fa5e8cd94b932ca9dfdc93399b126c1d138df934
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Astronomy and Astrophysics
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry (2015, methodology): “We also point out that compared to [19, 24, 21, 23] we denote by mμ here what was referred to as m̃μ in these papers and vice versa we denote by m̃μ here what was denoted by mμ in these respective works.”
- Gauging the Carroll algebra and ultra-relativistic gravity (2015, methodology): “The Newton–Cartan dual of M is a covector Mμ that can be written as mμ − ∂μχ where mμ is the connection corresponding to the Bargmann extension of the Galilei algebra and χ is a Stückelberg scalar that must be added to the formalism whenever there is torsion [1, 2, 15].”
- Lifshitz space–times for Schrödinger holography (2014, methodology): “We refer to Φ̃ as the Newton’s potential for reasons explained in [9].”
- Lifshitz holography (2015, unknown): “Torsional Newton-Cartan structure (TNC) is particularly relevant for holography, see [123, 126, 127, 128].”