Some exact BPS solutions for exotic vortices and monopoles. (English) Zbl 1365.81084
Summary: We present several analytical solutions of BPS vortices and monopoles in the generalized abelian Maxwell-Higgs and Yang-Mills-Higgs theories, respectively. These models have recently been extensively studied and several exact solutions have already been obtained in [R. Casana et al., “Analytical BPS Maxwell-Higgs vortices”, Adv. High Energy Phys. 2014, 1–9 (2014; doi:10.1155/2014/210929); “Analytical self-dual solutions in a nonstandard Yang-Mills-Higgs scenario”, Phys. Lett. B 722, No. 1–3, 193–197 (2013; doi:10.1016/j.physletb.2013.04.023)]. In each theory, the dynamics is controlled by the additional two positive scalar-field-dependent functions, \(f(| \phi |)\) and \(w(| \phi |)\). For the case of vortices, we work in the ordinary symmetry-breaking Higgs potential, while for the case of monopoles we have the ordinary condition of the Prasad-Sommerfield limit. Our results generalize the exact solutions found previously. We also present solutions for BPS vortices with higher winding number. These solutions suffer from the condition that \(w(| \phi |)\) has negative value at some finite range of \(r\), but we argue that since it satisfies the weaker positive-value conditions then the corresponding energy density is still positive-definite and, thus, they are acceptable BPS solutions.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81R40 | Symmetry breaking in quantum theory |
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