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

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.