Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure
arXiv:1005.0760 · doi:10.1007/JHEP07(2010)069
Abstract
We continue our study of the global properties of the z=2 Schroedinger space-time. In particular, we provide a codimension 2 isometric embedding which naturally gives rise to the previously introduced global coordinates. Furthermore, we study the causal structure by probing the space-time with point particles as well as with scalar fields. We show that, even though there is no global time function in the technical sense (Schroedinger space-time being non-distinguishing), the time coordinate of the global Schroedinger coordinate system is, in a precise way, the closest one can get to having such a time function. In spite of this and the corresponding strongly Galilean and almost pathological causal structure of this space-time, it is nevertheless possible to define a Hilbert space of normalisable scalar modes with a well-defined time-evolution. We also discuss how the Galilean causal structure is reflected and encoded in the scalar Wightman functions and the bulk-to-bulk propagator.
32 pages
References in corpus (9)
- Gravity duals for non-relativistic CFTs
- Boundary Conditions and Dualities: Vector Fields in AdS/CFT
- Holographic stress tensor for non-relativistic theories
- Correlation Functions in Non-Relativistic Holography
- Geometry of Schroedinger Space-Times, Global Coordinates, and Harmonic Trapping
- Chronological spacetimes without lightlike lines are stably causal
- Asymptotic symmetries of Schrödinger spacetimes
- Real-Time Correlators and Non-Relativistic Holography
- Scalar Field Probes of Power-Law Space-Time Singularities
Cited by in corpus (15)
- Holography for Schrodinger backgrounds
- Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum
- Stringy Schroedinger truncations
- Nonrelativistic conformal groups and their dynamical realizations
- Holography for chiral scale-invariant models
- Embedding nonrelativistic physics inside a gravitational wave
- Asymptotically Schroedinger Space-Times: TsT Transformations and Thermodynamics
- Extending the nonsingular hyperscaling violating spacetimes
- Black Probes of Schrödinger Spacetimes
- Particle Number and 3D Schroedinger Holography
- Holographic real-time non-relativistic correlators at zero and finite temperature
- Unitary representations of N-conformal Galilei group
- Hidden horizons in non-relativistic AdS/CFT
- The Godel-Schrodinger Spacetime and Stringy Chronology Protection
- Asymptotically Schrödinger Space-Times