Signature Change of the Metric in CDT Quantum Gravity?

TL;DR

This paper investigates the effective transfer matrix in CDT quantum gravity, revealing a sign change in the kinetic term across phases that suggests a metric Wick rotation, and proposes an order parameter to study phase transitions.

Contribution

It introduces an analysis of the transfer matrix sign change as a potential metric Wick rotation and proposes an order parameter to locate phase transitions in CDT quantum gravity.

Findings

Sign change in the kinetic term indicates a Wick rotation of the metric.

Proposed an order parameter to identify the bifurcation phase transition.

Updated the CDT phase diagram with the transition location.

Abstract

We study the effective transfer matrix within the semiclassical and bifurcation phases of CDT quantum gravity. We find that for sufficiently large lattice volumes the kinetic term of the effective transfer matrix has a different sign in each of the two phases. We argue that this sign change can be viewed as a Wick rotation of the metric. We discuss the likely microscopic mechanism responsible for the bifurcation phase transition, and propose an order parameter that can potentially be used to determine the precise location and order of the transition. Using the effective transfer matrix we approximately locate the position of the bifurcation transition in some region of coupling constant space, allowing us to present an updated version of the CDT phase diagram.