Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 7, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP07(2010)069
Keywords
AdS-CFT Correspondence; Gauge-gravity correspondence; Space-Time Symmetries
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Funding
- Swiss National Science Foundation
- Schweizerische Universitatskonferenz SUK/CUS
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We continue our study of the global properties of the z = 2 Schrodinger 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 (Schrodinger space-time being non-distinguishing), the time coordinate of the global Schrodinger 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.
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