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Holography for the Lorentz Group Racah Coefficients

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Kirill Krasnov

General Relativity and Quantum Cosmology · Submitted 21 Dec 2004

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv IDgr-qc/0412104 (version 3)
Pith ID7PFXGTJB, Pith's permanent record of this paper and its review
CitationKirill Krasnov. "Holography for the Lorentz Group Racah Coefficients." arXiv:gr-qc/0412104 (2004). https://pith.science/paper/7PFXGTJB
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,517 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.90 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. background 1.00 0.05 0.09 asserted 1.00
s1 These are ``bulk-to-bulk'' propagators in that they are functions of two points in the hyperbolic space. background 1.00 0.06 0.03 asserted 1.00
s2 It is known that the bulk-to-bulk propagator can be constructed out of two bulk-to-boundary ones. background 1.00 0.04 0.03 asserted 1.00
s3 We point out that there is another way to obtain the same object. contribution 0.85 0.70 0.08 asserted 0.80
s4 Namely, one can use two bulk-to-boundary and one boundary-to-boundary propagator. contribution 0.52 0.53 0.16 asserted 0.62
s5 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. result 0.54 0.93 0.71 asserted 1.00
s6 This holographic realization admits a geometric interpretation in terms of an ``extended'' tetrahedron. interpretation 0.99 0.82 0.24 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.91 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

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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2 arXiv papers cite this in 3 sentences

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