Geometry of Schroedinger Space-Times, Global Coordinates, and Harmonic Trapping

Abstract

We study various geometrical aspects of Schroedinger space-times with dynamical exponent z>1 and compare them with the properties of AdS (z=1). The Schroedinger metrics are singular for 1<z<2 while the usual Poincare coordinates are incomplete for z \geq 2. For z=2 we obtain a global coordinate system and we explain the relations among its geodesic completeness, the choice of global time, and the harmonic trapping of non-relativistic CFTs. For z>2, we show that the Schroedinger space-times admit no global timelike Killing vectors.

15 pages, v2: some comments and references added

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Cited by in corpus (46)

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• Lifshitz spacetimes from AdS null and cosmological solutions
• Holography for Schrodinger backgrounds
• A Jordanian deformation of AdS space in type IIB supergravity
• Anisotropic Conformal Infinity
• Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum
• From D3-Branes to Lifshitz Space-Times
• Hyperscaling violating black holes with spherical and hyperbolic horizons
• Stringy Schroedinger truncations
• Two Virasoro symmetries in stringy warped AdS${}_3$
• Integrability in dipole-deformed N=4 super Yang-Mills
• Super Galilean conformal algebra in AdS/CFT
• The Curious Case of Null Warped Space
• Non-relativistic metrics with extremal limits
• Embedding nonrelativistic physics inside a gravitational wave
• Schrodinger invariant solutions of M-theory with Enhanced Supersymmetry
• Below the Breitenlohner-Freedman bound in the nonrelativistic AdS/CFT correspondence
• Aspects of Non-Relativistic Quantum Field Theories
• A Note on Black Holes in Asymptotically Lifshitz Spacetime
• String theories on warped AdS backgrounds and integrable deformations of spin chains
• Asymptotic symmetries of Schrödinger spacetimes
• New (p+1) Dimensional Non-relativistic Theories from Euclidean Stable and Unstable Dp-Branes
• Schrödinger Manifolds
• Asymptotically Schroedinger Space-Times: TsT Transformations and Thermodynamics
• Critical solutions in topologically gauged N=8 CFTs in three dimensions
• Quantum corrections to extremal black brane solutions
• Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure
• Extending the nonsingular hyperscaling violating spacetimes
• Particle Number and 3D Schroedinger Holography
• Holographic three-point correlators in the Schrodinger/dipole CFT correspondence
• Black Probes of Schrödinger Spacetimes
• Semiclassical spectrum of a Jordanian deformation of $Ad{S}_5\times S^5$
• Hidden horizons in non-relativistic AdS/CFT
• Open String in Non-Relativistic Background
• Dynamical realizations of the Lifshitz group
• The Godel-Schrodinger Spacetime and Stringy Chronology Protection
• Nernst branes with Lifshitz asymptotics in N=2 gauged supergravity
• Asymptotically Schrödinger Space-Times
• Anisotropic Schrödinger black holes with hyperscaling-violation
• Revisiting Wilson loops for nonrelativistic backgrounds
• On Pulsating Strings in Schrödinger Backgrounds
• Pulsating strings in $Sch{r}_5\times T^{1,1}$ background
• Giant Gravitons in the Schrodinger holography
• Penrose Limit and Non-relativistic geometries
• Jordanian spin chains for twisted strings in $Ad{S}_5\times S^5$
• Note About Hamiltonian Dynamics of String in Non-Relativistic D3-Brane Background