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’).
T. Regge, General relativity without coordinates, Nuovo Cim. 19 (1961) 558 [INSPIRE].
F. David, Planar diagrams, two-dimensional lattice gravity and surface models, Nucl. Phys. B 257 (1985) 45 [INSPIRE].
V.A. Kazakov, A.A. Migdal and I.K. Kostov, Critical properties of randomly triangulated planar random surfaces, Phys. Lett. B 157 (1985) 295 [INSPIRE].
J. Ambjørn, B. Durhuus and J. Fröhlich, Diseases of triangulated random surface models and possible cures, Nucl. Phys. B 257 (1985) 433 [INSPIRE].
J. Ambjorn, B. Durhuus, J. Frohlich and P. Orland, The appearance of critical dimensions in regulated string theories, Nucl. Phys. B 270 (1986) 45.
D.V. Boulatov, V.A. Kazakov, I.K. Kostov and A.A. Migdal, Analytical and numerical study of the model of dynamically triangulated random surfaces, Nucl. Phys. B 275 (1986) 641 [INSPIRE].
V.G. Knizhnik, A.M. Polyakov and A.B. Zamolodchikov, Fractal structure of 2D quantum gravity, Mod. Phys. Lett. A 3 (1988) 819 [INSPIRE].
F. David, Conformal field theories coupled to 2D gravity in the conformal gauge, Mod. Phys. Lett. A 3 (1988) 1651 [INSPIRE].
J. Distler and H. Kawai, Conformal field theory and 2D quantum gravity or who’s afraid of Joseph Liouville?, Nucl. Phys. B 321 (1989) 509 [INSPIRE].
J. Ambjørn and S. Varsted, Entropy estimate in three-dimensional simplicial quantum gravity, Phys. Lett. B 266 (1991) 285 [INSPIRE].
M.E. Agishtein and A.A. Migdal, Three-dimensional quantum gravity as dynamical triangulation, Mod. Phys. Lett. A 6 (1991) 1863 [Erratum ibid. A 6 (1991) 2555] [INSPIRE].
D.V. Boulatov and A. Krzywicki, On the phase diagram of three-dimensional simplicial quantum gravity, Mod. Phys. Lett. A 6 (1991) 3005 [INSPIRE].
J. Ambjørn, D.V. Boulatov, A. Krzywicki and S. Varsted, The vacuum in three-dimensional simplicial quantum gravity, Phys. Lett. B 276 (1992) 432 [INSPIRE].
J. Ambjørn and S. Varsted, Three-dimensional simplicial quantum gravity, Nucl. Phys. B 373 (1992) 557 [INSPIRE].
J. Ambjørn and J. Jurkiewicz, Four-dimensional simplicial quantum gravity, Phys. Lett. B 278 (1992) 42 [INSPIRE].
M.E. Agishtein and A.A. Migdal, Simulations of four-dimensional simplicial quantum gravity, Mod. Phys. Lett. A 7 (1992) 1039 [INSPIRE].
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.
ArXiv ePrint: 1403.5940
About this article
Cite this article
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
- Models of Quantum Gravity
- Random Systems
- Lattice Models of Gravity