Numerical Study of Periodic Instanton Configurations in Two-dimensional Abelian Higgs Theory

TL;DR

This paper numerically investigates periodic instanton configurations in the two-dimensional Abelian Higgs model, revealing their properties across energy ranges and their implications for multiparticle scattering probabilities.

Contribution

It introduces a numerical method to construct and analyze periodic instantons in the Abelian Higgs model, detailing their action and energy dependence on period.

Findings

Periodic instantons exist at all energies up to sphaleron energy.

The action and energy depend on the instanton period.

Results inform probabilities of multiparticle scattering events.

Abstract

Numerical minimization of the Euclidean action of the two-dimensional Abelian Higgs model is used to construct periodic instantons, the euclidean field configurations with two turning points describing transitions between the vicinities of topologically distinct vacua. Periodic instantons are found at any energy ( up to the sphaleron energy $E_{sph}$ ) and for wide range of parameters of the theory. We obtain the dependence of the action and the energy of periodic instanton on its period; these quantities directly determine the probability of certain multiparticle scattering events.