Holography for the Lorentz Group Racah Coefficients

Details Holography for the Lorentz Group Racah Coefficients Holography for the Lorentz Group Racah Coefficients

2004-12-21

arxiv.org/abs/gr-qc/0412104v3

Class.Quant.Grav. 22 (2005) 1933-1944

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, 2 figures; v2: minor changes; v3: "extended" tetrahedron interpretation added

Scientific paper

10.1088/0264-9381/22/11/003

A 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.

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