Tunneling decay of false kinks

TL;DR

This paper analyzes the decay process of false kinks in a scalar field theory with degenerate vacua, deriving decay rates and highlighting conditions where kinks can significantly accelerate vacuum decay.

Contribution

It provides a new expression for the decay rate of false kinks and explores parameter regimes where these kinks become nearly unstable, impacting vacuum longevity.

Findings

Decay rate depends exponentially on Euclidean action S_E.

S_E can become arbitrarily small for certain parameters.

False kinks can induce rapid vacuum decay despite a long-lived false vacuum.

Abstract

We consider the decay of "false kinks," that is, kinks formed in a scalar field theory with a pair of degenerate symmetry-breaking false vacua in 1+1 dimensions. The true vacuum is symmetric. A second scalar field and a peculiar potential are added in order for the kink to be classically stable. We find an expression for the decay rate of a false kink. As with any tunneling event, the rate is proportional to $\exp(-S_E)$ where $S_E$ is the Euclidean action of the bounce describing the tunneling event. This factor varies wildly depending on the parameters of the model. Of interest is the fact that for certain parameters $S_E$ can get arbitrarily small, implying that the kink is only barely stable. Thus, while the false vacuum itself may be very long-lived, the presence of kinks can give rise to rapid vacuum decay.