Foundations of Physics

, Volume 42, Issue 7, pp 909–917 | Cite as

Holography in the EPRL Model

  • Louis Crane


In this research announcement, we propose a new interpretation of the Engle Pereira Rovelli (EPR) quantization of the Barrett-Crane (BC) model using a functor we call the time functor, which is the first example of a co-lax, amply renormalizable (claren) functor. Under the hypothesis that the universe is in the Kodama state, we construct a holographic version of the model. Generalisations to other claren functors and connections to model category theory are considered.


Quantum gravity Topological quantum field theory Model category theory 


  1. 1.
    Engle, J., Pereira, R., Rovelli, C.: Flipped spinfoam vertex and loop gravity. Nucl. Phys. B 798(1–2), 251–290 (2008) MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    Livine, E.R., Speziale, S.: New spinfoam vertex for quantum gravity. Phys. Rev. D 76, 084028 (2007) MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    Pereira, R.: Lorentzian LQG vertex amplitude. Class. Quantum Gravity 085013 (2008) Google Scholar
  4. 4.
    Barrett, J.W., Dowdall, R.J., Fairbairn, W.J., Gomes, H., Hellmann, F.: Asymptotic analysis of the Engle Pereira Rovelli Livine four-simplex amplitude. J. Math. Phys. 50, 112504 (2009) MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    Barrett, J., Crane, L.: A Lorentzian signature model for quantum gravity. Class. Quantum Gravity 17, 3101–3118 (2000) MathSciNetADSMATHCrossRefGoogle Scholar
  6. 6.
    Bousso, R.: The holographic principle. Rev. Mod. Phys. 74, 825–874 (2002) MathSciNetADSMATHCrossRefGoogle Scholar
  7. 7.
    Crane, L.: 2d physics and 3d topology. Commun. Math. Phys. 135, 615–640 (1991) MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    Baez, J.C., Barrett, J.W.: Integrability for relativistic spin networks. Class. Quantum Gravity 18, 4683 (2001) MathSciNetADSMATHCrossRefGoogle Scholar
  9. 9.
    Crane, L., Yetter, D.: A categorical construction of 4D topological quantum field theories. Quantum Topol. 120–129 (1993) Google Scholar
  10. 10.
    Witten, E.: Topological quantum field theory and the Jones polynomial. Commun. Math. Phys. 121, 351 (1989) MathSciNetADSMATHCrossRefGoogle Scholar
  11. 11.
    Kodama, H.: Holomorphic wave function of the Universe. Phys. Rev. D 42, 2548–2565 (1990) MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Bekenstein, J.D.: Holographic bound from second law of thermodynamics. Phys. Lett. B 481(2–4), 339–345 (2000) MathSciNetADSMATHGoogle Scholar
  13. 13.
    Smolin, L.: An invitation to loop quantum gravity (2004). hep-th/0408048
  14. 14.
    Crane, L.: Relational spacetime, model categories and quantum gravity. Int. J. Mod. Phys. A 24(15), 2753–2775 (2009) MathSciNetADSMATHCrossRefGoogle Scholar
  15. 15.
    Bousfield, A.K., Kan, D.M.: Homotopy limits, completions and localizations (1972) Google Scholar
  16. 16.
    Sullivan, D.: Infinitesimal computations in topology. Publ. Math. IHES 47(1), 269–331 (1977) MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Mathematics DepartmentKSUManhattanUSA

Personalised recommendations