Metastable Strings in Abelian Higgs Models Embedded in Non-Abelian Theories: Calculating the Decay Rate

TL;DR

This paper investigates the metastability and decay rate of U(1) strings embedded in non-Abelian gauge theories with hierarchical symmetry breaking, providing a calculation of the decay rate based on an effective world-sheet theory.

Contribution

It introduces a novel ansatz for unwinding embedded strings and derives a general formula for their decay rate, connecting monopole mass and string tension.

Findings

Decay rate is exponentially suppressed by the ratio of monopole mass squared to string tension.

The decay process involves monopole-antimonopole pair production.

The derived formula aligns with Schwinger's pair production mechanism.

Abstract

We study the fate of U(1) strings embedded in a non-Abelian gauge theory with a hierarchical pattern of the symmetry breaking: G->U(1) at V->nothing at v, V>>v. While in the low-energy limit the Abrikosov-Nielsen-Olesen string (flux tube) is perfectly stable, being considered in the full theory it is metastable. We consider the simplest example: the magnetic flux tubes in the SU(2) gauge theory with adjoint and fundamental scalars. First, the adjoint scalar develops a vacuum expectation value V breaking SU(2) down to U(1). Then, at a much lower scale, the fundamental scalar (quark) develops a vacuum expectation value v creating the Abrikosov-Nielsen-Olesen string. (We also consider an alternative scenario in which the second breaking, U(1)->nothing, is due to an adjoint field.) We suggest an illustrative ansatz describing an "unwinding" in SU(2) of the winding inherent to the Abrikosov-Nielsen-Olesen strings in U(1). This ansatz determines an effective 2D theory for the unstable mode on the string world-sheet. We calculate the decay rate (per unit length of the string) in this ansatz and then derive a general formula. The decay rate is exponentially suppressed. The suppressing exponent is proportional to the ratio of the monopole mass squared to the string tension, which is quite natural in view of the string breaking through the monopole-antimonopole pair production. We compare our result with the one given by Schwinger's formula dualized for describing the monopole-antimonopole pair production in the magnetic field.