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

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').

33 pages, 24 figures

References in corpus (3)

• Nonperturbative Quantum Gravity
• The Semiclassical Limit of Causal Dynamical Triangulations
• The Emergence of Spacetime, or, Quantum Gravity on Your Desktop

Cited by in corpus (5)

• The microscopic structure of 2D CDT coupled to matter
• Spectral Methods and Running Scales in Causal Dynamical Triangulations
• Topology induced first-order phase transitions in lattice quantum gravity
• The spectral dimension in 2D CDT gravity coupled to scalar fields
• The phase structure and effective action of 3D CDT at higher spatial genus