Poincaré coordinates
E590884
Poincaré coordinates are a commonly used coordinate system on anti-de Sitter space that makes its conformal boundary manifestly Minkowskian and is especially convenient in AdS/CFT calculations.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
coordinate system
ⓘ
mathematical concept ⓘ |
| appearsIn |
quantum gravity in AdS space
ⓘ
string theory on AdS backgrounds ⓘ supergravity solutions on AdS ⓘ |
| associatedWith |
Poincaré group on the boundary
ⓘ
conformal boundary of AdS ⓘ |
| boundaryDimension | d ⓘ |
| boundaryLocatedAt | z = 0 ⓘ |
| boundaryMetric | eta_{ mu u} dx^{ mu} dx^{ u} ⓘ |
| boundarySignature | Minkowski NERFINISHED ⓘ |
| bulkRegion | z > 0 ⓘ |
| coordinateRange |
t
in
(-
i
nfty,
+
i
nfty)
ⓘ
x^i in (- i nfty, + i nfty) ⓘ z > 0 ⓘ |
| dimensionConvention | bulk dimension d+1 ⓘ |
| hasBoundaryCoordinates | x^{ mu} ⓘ |
| hasParameter | AdS radius L ⓘ |
| hasProperty |
adapted to AdS/CFT correspondence
ⓘ
conformally flat boundary metric ⓘ covers only a patch of global AdS ⓘ makes conformal boundary manifestly Minkowskian ⓘ often called Poincaré patch coordinates ⓘ |
| hasRadialCoordinate | z ⓘ |
| hasSpatialCoordinates | vec{x} ⓘ |
| hasTimeCoordinate | t ⓘ |
| induces | flat Minkowski metric on the boundary up to a conformal factor ⓘ |
| metricDependsOn | AdS radius L ⓘ |
| metricForm | ds^2 = (L^2/z^2)(dz^2 + eta_{ mu u} dx^{ mu} dx^{ u}) ⓘ |
| namedAfter | Henri Poincaré NERFINISHED ⓘ |
| relatedTo |
Fefferman–Graham coordinates
NERFINISHED
ⓘ
global AdS coordinates ⓘ |
| simplifies |
Fourier transforms along boundary directions
ⓘ
asymptotic analysis near AdS boundary ⓘ identification of boundary field theory ⓘ |
| usedFor |
constructing AdS black brane solutions
ⓘ
finite-temperature AdS/CFT setups ⓘ holographic RG flows ⓘ holographic hydrodynamics ⓘ studying conformal field theories on Minkowski space ⓘ |
| usedIn |
AdS/CFT calculations
ⓘ
Witten diagrams NERFINISHED ⓘ bulk-to-boundary propagators ⓘ gauge/gravity duality NERFINISHED ⓘ holographic correlation functions ⓘ holographic entanglement entropy ⓘ holographic renormalization ⓘ |
| usedOn |
AdS_{d+1}
ⓘ
anti-de Sitter space NERFINISHED ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.