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The effective action in 4-dim CDT. The transfer matrix approach

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  • Published: 06 June 2014
  • volume 2014, Article number: 34 (2014)
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The effective action in 4-dim CDT. The transfer matrix approach
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  • J. Ambjørn1,2,
  • J. Gizbert-Studnicki3,
  • A. Görlich1,3 &
  • …
  • J. Jurkiewicz3 

  • 369 Accesses

  • 27 Citations

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A preprint version of the article is available at arXiv.

Abstract

We measure the effective action in all three phases of 4-dimensional Causal Dynamical Triangulations (CDT) using the transfer matrix method. The transfer matrix is parametrized by the total 3-volume of the CDT universe at a given (discrete) time. We present a simple effective model based on the transfer matrix measured in the de Sitter phase. It allows us to reconstruct the results of full CDT in this phase. We argue that the transfer matrix method is valid not only inside the de Sitter phase (‘C’) but also in the other two phases. A parametrization of the measured transfer matrix/effective action in the ‘A’ and ‘B’ phases is proposed and the relation to phase transitions is explained. We discover a potentially new ‘bifurcation’ phase separating the de Sitter phase (‘C’) and the ‘collapsed’ phase (‘B’).

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Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

  1. The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark

    J. Ambjørn & A. Görlich

  2. IMAPP, Radboud University, Niemegen, The Netherlands

    J. Ambjørn

  3. Institute of Physics, Jagellonian University, Reymonta 4, PL 30-059, Krakow, Poland

    J. Gizbert-Studnicki, A. Görlich & J. Jurkiewicz

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  1. J. Ambjørn
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Correspondence to J. Gizbert-Studnicki.

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ArXiv ePrint: 1403.5940

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Ambjørn, J., Gizbert-Studnicki, J., Görlich, A. et al. The effective action in 4-dim CDT. The transfer matrix approach. J. High Energ. Phys. 2014, 34 (2014). https://doi.org/10.1007/JHEP06(2014)034

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  • Received: 25 March 2014

  • Revised: 16 May 2014

  • Accepted: 16 May 2014

  • Published: 06 June 2014

  • DOI: https://doi.org/10.1007/JHEP06(2014)034

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Keywords

  • Models of Quantum Gravity
  • Random Systems
  • Lattice Models of Gravity
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