Abstract

We find both analytical and numerical solutions of SU(2) Yang-Mills with an adjoint Higgs field within both closed and open tubes whose sections are spherical caps. This geometry admits a smooth limit in which the space-like metric is flat and, moreover, allows one to use analytical tools which in the flat case are not available. Some of the analytic configurations, in the limit of vanishing Higgs coupling, correspond to magnetic monopoles and dyons living within this tube-shaped domain. However, unlike what happens in the standard case, analytical solutions can also be found in the case in which the Higgs coupling is non-vanishing. We further show that the system admits long-lived breathers.

Highlights

  • To address this issue, is a generalization of the usual hedgehog ansatz used in [1, 2]

  • One could think of placing the system whose action is given by eq (2.1) in a box, this would provide an explicit cut-off at the cost of loss of spherical symmetry of the hedgehog-like configurations

  • The Yang-Mills-Higgs system in the geometry described by the metric in eq (2.4) admits breather solutions which remain in an oscillatory state for a long time, with minimal emission of radiation

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Summary

The system

Which are, at the same time, spherically symmetric (which is very convenient from the analytical point of view) and can have the shape of (both closed and open) cylinders (which is important from the point of view of concrete applications: see [4, 12] and references therein) These considerations show that the choice of the metric eq (2.4), both with the complete range of angular coordinates eq (2.5) and with the restricted one eq (2.6), besides being interesting from the geometrical point of view is significant in relation to more applied models. The system whose action is eq (2.1) in the case of vanishing Higgs potential λ = 0 admits a BPS completion with the BPS inequality saturated by monopoles with mass equal to their magnetic charge, M = QM [13] In this case the Higgs and gauge fields are related by a first order BPS equation.

Magnetic solutions
Zero modes
Numerical solutions
The special point
Long-lived breathers
Dyonic solutions
Conclusions
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