Characteristics of the new phase in CDT

TL;DR

This paper explores the phase structure of Causal Dynamical Triangulations (CDT) in quantum gravity, focusing on the bifurcation phase and its transitions, revealing insights into the underlying mechanisms and physical implications.

Contribution

It provides a detailed analysis of the bifurcation phase in CDT, clarifies the nature of phase transitions, and links the new phase to the emergence of singular vertices affecting homogeneity.

Findings

The B-C_b transition is compatible with a second-order phase transition.

The C_b-C_dS transition is associated with the appearance of singular vertices.

The bifurcation phase breaks homogeneity and isotropy in the de Sitter phase.

Abstract

Causal Dynamical Triangulations (CDT), a candidate theory of nonperturbative quantum gravity in 4D, turns out to have a rich phase structure. We investigate the recently discovered bifurcation phase $C_b$ and relate some of its characteristics to the presence of singular vertices of very high order. The transition lines separating this phase from the "time-collapsed" $B$-phase and the de Sitter phase $C_{dS}$ are of great interest when searching for physical scaling limits. The work presented here sheds light on the mechanisms behind these transitions. First, we study how the $B$-$C_b$ transition signal depends on the volume-fixing implemented in the simulations, and find results compatible with the previously determined second-order character of the transition. The transition persists in a transfer matrix formulation, where the system's time extension is taken to be minimal. Second, we relate the new $C_b$-$C_{dS}$ transition to the appearance of singular vertices, which leads to a direct physical interpretation in terms of a breaking of the homogeneity and isotropy observed in the de Sitter phase when crossing from $C_{dS}$ to the bifurcation phase $C_b$.