Shape Is Destiny II: Configurational Information Approach to Instantons and False Vacuum Decay in D-dimensional Spacetime

TL;DR

This paper extends configurational information measures to analyze instantons and vacuum decay across arbitrary dimensions, revealing a critical dimension at D=6 and linking informational complexity to decay rates.

Contribution

It introduces a novel application of configurational information measures to instantons in arbitrary dimensions, identifying a critical dimension and relating complexity to decay rates.

Findings

Identifies a critical dimension at D=6 where instanton behavior changes.

Establishes a scaling law linking informational measures to vacuum decay rates.

Discriminates between thin and thick wall instanton profiles using complexity measures.

Abstract

We extend the use of Configurational Information Measures (CIMSs) to instantons and vacuum decay in arbitrary spatial dimensions. We find that both the complexity and the information content in the shape of instanton solutions have distinct regions of behavior in parameter space, discriminating between qualitative thin and thick wall profiles. For Euclidean spaces of dimension $D$, we show that for $D \gt 6$ instantons undergo a qualitative change of behavior from their lower- dimensional counterparts, indicating that $D=6$ is a critical dimension. We also find a scaling law relating the different CIMs to the rate of vacuum decay, thus connecting the stability of the vacuum to the informational complexity stored in the shape of the related critical bounce.