Abstract
We extend the use of configurational information measures (CIMs) 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 $D\ensuremath{\ge}6$ 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.
Highlights
Information theory made its debut in 1948 with Claude Shannon’s revolutionary A Mathematical Theory of Communication [1]
In this paper we have applied the framework of configurational information measures (CIMs) to instantons in a scalar field theory in D spacetime dimensions with an asymmetric double-well potential
We have focused on the DCC of these profiles in order to understand the informational complexity inherent to their shapes
Summary
Information theory made its debut in 1948 with Claude Shannon’s revolutionary A Mathematical Theory of Communication [1]. In it Shannon was able to quantify information, and, in particular, how it can be transferred from source to receiver through a generalized communication channel In so doing, he proved the celebrated noiseless and noisy coding theorems. Configurational information measures (CIMs) have grown out of the desire to quantify the informational content and complexity contained in the shape of physical structures naturally occurring in field theories. We will add to the phenomenology of CIMs by elucidating the informational narrative of false-vacuum decay via instanton tunneling. The idea that the vacuum could spontaneously decay into a lower energy state, or that it might have done so in the early Universe, suggests that instantons are relevant in a cosmological context [34] This was the original motivation of Guth’s first model of inflation [35], and many that followed. In the Appendix we present the calculation of the instanton action in D Euclidean dimensions in the thin-wall limit
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