Dynamical Generation of Spacetime Signature by Massive Quantum Fields on a Topologically Non-Trivial Background

TL;DR

This paper investigates how quantum effects of massive fields on a non-trivial topology can dynamically generate and prefer a Lorentzian spacetime signature, especially in compactified dimensions, with stability under perturbations.

Contribution

It demonstrates that quantum effects induce a dynamical Wick field favoring Lorentzian signature in certain compactified backgrounds, extending previous understanding of spacetime signature dynamics.

Findings

Lorentzian signature is preferred at small compactification radius.

Lorentzian signature remains stable at larger radii in 4D and 6D.

Results are robust under metric perturbations.

Abstract

The effective potential for a dynamical Wick field (dynamical signature) induced by the quantum effects of massive fields on a topologically non-trivial $D$ dimensional background is considered. It is shown that when the radius of the compactified dimension is very small compared with $\Lambda^{1/2}$ (where $\Lambda$ is a proper-time cutoff), a flat metric with Lorentzian signature is preferred on ${\bf R}^4 \times {\bf S}^1$. When the compactification radius becomes larger a careful analysis of the 1-loop effective potential indicates that a Lorentzian signature is preferred in both $D=6$ and $D=4$ and that these results are relatively stable under metrical perturbations.