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 Lifshitz space-times. We define an energy-momentum
tensor and a mass current and study the relation between conserved currents and
conformal Killing vectors for flat Newton-Cartan backgrounds. It is shown that
flat NC space-time realizes two copies of the Lifshitz algebra that together
form a Schroedinger algebra (without the central element). We show why the
Schroedinger scalar model has both copies as symmetries and the Lifshitz scalar
model only one. Finally we discuss the holographic dual of this phenomenon by
showing that the bulk Lifshitz space-time realizes the same two copies of the
Lifshitz algebra.Comment: 5 pages, modified abstract, clarifications added, typos fixed, refs
  update

Hamann, Bernd

Joy, Ken

LaMar, Eric C.

Nuber, Christof

English

arXiv

Hartong, Jelle

Kiritsis, Elias

Obers, Niels

HAL-OBSPM

Schrödinger invariance from Lifshitz isometries in holography and field theory

Obers, Niels A.

Copenhagen University Research Information System

Schrodinger invariance from Lifshitz isometries in holography and field theory

We extend the notion of multiresolution spatial data approximation of static datasets to spatio-temporal approximation of time-varying datasets. By including a temporal component, we allow a region from one time-step to approximate a congruent region at another time-step. While approximations of static datasets are generated by refining the representation if a given error-bound is not met, for approximations of time-varying datasets we use data from another time-step, if that data meets a given error-bound for the current time-step. Thus, our technique exploits the fact that time-varying datasets typically do not change uniformly over time, and by only loading data from rapidly changing regions, much less data need be loaded to generate an approximation. Regions that don't change, or change slowly, are not loaded and are approximated by regions from another time-step. Prior techniques only permit binary classifications between  consecutive time-steps.  Our technique allows a run-time error-criterion between non-temporally consecutive time-steps. Error between time-steps is calculated in a pre-processing step and stored in error-tables.  These error-tables are used to calculate error at run-time, so no data is touched. User movements in time are not restricted to unidirectional, successive changes - movement can be forward, backward, or to any arbitrary time-step

eScholarship - University of California

Approximating time-varying multiresolution data using error-based temporal-spatial reuse

We extend the notion of multi-resolution spatial data approximation of static datasets to spatio-temporal approximation of time-varying datasets. By including the temporal dimension, we allow a region of one time-step to approximate a congruent region at another time-step. Approximations of static datasets are generated by refining an approximation until a given error-bound is met. To approximate time-varying datasets we use data from another time-step when that data meets a given error-bound for the current time-step. Our technique exploits the fact that time-varying datasets typically do not change uniformly over time. By loading data from rapidly changing regions only, less data needs to be loaded to generate an approximation. Regions that hardly change are not loaded and are approximated by regions from another time-step. Typically, common techniques only permit binary classification between consecutive time-steps. Our technique allows a run-time error-criterion to be used between non-temporally consecutive time-steps. The errors between time-steps are calculated in a pre-processing step and stored in error-tables. These error-tables are used to calculate errors at run-time, thus no data needs to be accessed

Christof Nuber

Eric C. LaMar

Bernd Hamann

Kenneth I. Joy

CiteSeerX

Approximation of Time-varying Multi-resolution Data Using Error-based Temporal-spatial Reuse

Jelle Hartong

Elias Kiritsis

Niels A. Obers

Crossref

Physical Review D

HAL-CEA

HAL-IN2P3

Hal-Diderot

https://escholarship.org/content/qt0vx3v0g9/qt0vx3v0g9.pdf?t=prjrqs