forgot password?
register here
Research articles
  search articles
  reviews guidelines
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
Members: 3431
Articles: 2'256'574
Articles rated: 2602

25 September 2022
  » arxiv » 0905.3627

 Article overview

Holomorphic Factorization for a Quantum Tetrahedron
Laurent Freidel ; Kirill Krasnov ; Etera R. Livine ;
Date 22 May 2009
AbstractWe provide a holomorphic description of the Hilbert space H(j_1,..,j_n) of SU(2)-invariant tensors (intertwiners) and establish a holomorphically factorized formula for the decomposition of identity in H(j_1,..,j_n). Interestingly, the integration kernel that appears in the decomposition formula turns out to be the n-point function of bulk/boundary dualities of string theory. Our results provide a new interpretation for this quantity as being, in the limit of large conformal dimensions, the exponential of the Kahler potential of the symplectic manifold whose quantization gives H(j_1,..,j_n). For the case n=4, the symplectic manifold in question has the interpretation of the space of "shapes" of a geometric tetrahedron with fixed face areas, and our results provide a description for the quantum tetrahedron in terms of holomorphic coherent states. We describe how the holomorphic intertwiners are related to the usual real ones by computing their overlap. The semi-classical analysis of these overlap coefficients in the case of large spins allows us to obtain an explicit relation between the real and holomorphic description of the space of shapes of the tetrahedron. Our results are of direct relevance for the subjects of loop quantum gravity and spin foams, but also add an interesting new twist to the story of the bulk/boundary correspondence.
Source arXiv, 0905.3627
Services Forum | Review | PDF | Favorites   
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
of broad interest:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

browser CCBot/2.0 (
» my Online CV
» Free

News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2022 - Scimetrica