Tunneling decay of false vortices

Abstract

We consider the decay of vortices trapped in the false vacuum of a theory of scalar electrodynamics in 2+1 dimensions. The potential is inspired by models with intermediate symmetry breaking to a metastable vacuum that completely breaks a U(1) symmetry, while in the true vacuum the symmetry is unbroken. The false vacuum is unstable through the formation of true vacuum bubbles; however, the rate of decay can be extremely long. On the other hand, the false vacuum can contain metastable vortex solutions. These vortices contain the true vacuum inside in addition to a unit of magnetic flux and the appropriate topologically nontrivial false vacuum outside. We numerically establish the existence of vortex solutions which are classically stable; however, they can decay via tunneling. In general terms, they tunnel to a configuration which is a large, thin-walled vortex configuration that is now classically unstable to the expansion of its radius. We compute an estimate for the tunneling amplitude in the semi-classical approximation. We believe our analysis would be relevant to superconducting thin films or superfluids.Comment: 27 pages, 9 figure

Tunneling decay of false vortices with gravitation

“…In both cases, solutions obtained with different values of κ are plotted. The vortex profile for κ = 0 is in accordance with the previous study [7]. As gravity is added, matter fields do not change much compared to metric fields.…”

“…An energy barrier prevents the vortex from classically expanding to the escape radius R 1 from which it would explode; the vortex is quantum mechanically metastable. This feature of the system was observed in flat spacetime in [7] using different methods.…”

“…In earlier work [7], a metastable analog of the vortex dubbed a false vortex was studied. It owes its name to the vacuum structure permitting its formation.…”

“…The value of ǫ determines the shape of the potential [7,17]. The curvature scalar has mass dimension 2, 1/κ has mass dimension 1, the fields A µ and φ, the charge all have mass dimension 1/2, while the constants λ and ǫ are dimensionless parameters.…”

“…In the previous paper [7], it was shown that the difference between the false and true vacuum state, ǫ, is crucial for the metastability of the vortices. They become unstable above a certain critical value ǫ c .…”