Abstract
Abstract In monopole–antimonopole chain solutions of SU ( 2 ) Yang–Mills–Higgs theory the Higgs field vanishes at m isolated points along the symmetry axis, whereas in vortex ring solutions the Higgs field vanishes along one or more rings, centered around the symmetry axis. We investigate how these static axially symmetric solutions depend on the strength of the Higgs selfcoupling λ. We show, that as the coupling is getting large, new branches of solutions appear at critical values of λ. Exhibiting a different node structure, these give rise to transitions between vortex rings and monopole–antimonopole chains.
Highlights
The nontrivial vacuum structure of SU(2) Yang-Mills-Higgs (YMH) theory allows for the existence of regular non-perturbative finite mass solutions, such as spherically symmetric monopoles [1], axially symmetric multimonopoles [2, 3, 4, 5] and monopoleantimonopole pairs [6, 7]
When the Higgs field becomes massive, the fine balance of forces between the monopoles is broken since the corresponding attractive Yukawa interaction becomes short-ranged, and the non-BPS monopoles experience repulsion [5]
Based on the observations in the topologically trivial sector we expect a bifurcation at a critical value of λ, where two new branches of solutions appear, which possess a node structure different from the solutions on the fundamental branch
Summary
The nontrivial vacuum structure of SU(2) Yang-Mills-Higgs (YMH) theory allows for the existence of regular non-perturbative finite mass solutions, such as spherically symmetric monopoles [1], axially symmetric multimonopoles [2, 3, 4, 5] and monopoleantimonopole pairs [6, 7]. As shown by Taubes [11], each topological sector contains besides the (multi)monopole solutions further regular, finite mass solutions, which do not satisfy the first order Bogomol’nyi equations, but only the set of second order field equations, even for vanishing Higgs potential Such solutions, representing for instance static axially symmetric monopole-antimonopole chain and vortex ring configurations [8], form saddlepoints of the energy functional, and possess a mass above the Bogomol’nyi bound. They exist because the attractive short-range forces between the poles, that are mediated by the A3μ vector boson and the Higgs boson, are balanced by the repulsion, which is mediated by the massive vector bosons A±μ.
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