A second look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations

TL;DR

This paper challenges previous claims that Lorentzian geometries dominate in (2+1)-dimensional causal dynamical triangulations, providing evidence that the observed phenomena are consistent with Euclidean quantum geometries.

Contribution

It offers a new interpretation of earlier findings, arguing for the Euclidean nature of the quantum geometries and explaining the behavior of the Euclidean path integral in the semiclassical limit.

Findings

Evidence supports Euclidean rather than Lorentzian quantum geometries.

The Euclidean path integral behaves correctly in the semiclassical limit.

Multiple constraints influence the Euclidean quantum geometries.

Abstract

Studying transition amplitudes in (2+1)-dimensional causal dynamical triangulations, Cooperman and Miller discovered speculative evidence for Lorentzian quantum geometries emerging from its Euclidean path integral. On the basis of this evidence, Cooperman and Miller conjectured that Lorentzian de Sitter spacetime, not Euclidean de Sitter space, dominates the ground state of the quantum geometry of causal dynamical triangulations on large scales, a scenario akin to that of the Hartle-Hawking no-boundary proposal in which Lorentzian spacetimes dominate a Euclidean path integral. We argue against this conjecture: we propose a more straightforward explanation of their findings, and we proffer evidence for the Euclidean nature of these seemingly Lorentzian quantum geometries. This explanation reveals another manner in which the Euclidean path integral of causal dynamical triangulations behaves correctly in its semiclassical limit--the implementation and interaction of multiple constraints.