Tunneling decay of false kinks

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 $\mathrm{exp}(\ensuremath{-}{S}_{E})$ 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.