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

• Published in: The journal of high energy physics Vol. 2014; no. 6; pp. 1 - 29
• Main Authors: Ambjørn, J., Gizbert-Studnicki, J., Görlich, A., Jurkiewicz, J.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2014; Springer Nature B.V
• Subjects: Bifurcations; Classical and Quantum Gravitation; Elementary Particles; High energy physics; Parametrization; Phase transformations; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; String Theory; Three phase; Triangulation; Two phase; Universe; Lattice Models of Gravity; Random Systems; Models of Quantum Gravity
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2014)034

A bstract 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’).