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18 August 2022
 
  » arxiv » gr-qc/0412104

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Holography for the Lorentz Group Racah Coefficients
Kirill Krasnov ;
Date 21 Dec 2004
Journal Class.Quant.Grav. 22 (2005) 1933-1944
Subject gr-qc hep-th
AbstractA known realization of the Lorentz group Racah coefficients is given by an integral of a product of 6 ``propagators’’ over 4 copies of the hyperbolic space. These are ``bulk-to-bulk’’ propagators in that they are functions of two points in the hyperbolic space. It is known that the bulk-to-bulk propagator can be constructed out of two bulk-to-boundary ones. We point out that there is another way to obtain the same object. Namely, one can use two bulk-to-boundary and one boundary-to-boundary propagator. Starting from this construction and carrying out the bulk integrals we obtain a realization of the Racah coefficients that is ``holographic’’ in the sense that it only involves boundary objects. This holographic realization admits a geometric interpretation in terms of an ``extended’’ tetrahedron.
Source arXiv, gr-qc/0412104
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