Static cosmic strings on S2 and criticality

Research output: Contribution to journalArticle

Abstract

In this paper we construct static cosmic string solutions in the Bogomol'nyi phase of the Abelian Higgs model in an S2 setting. The strings are located at the north and south poles and have identical winding numbers. This construction, in particular, solves an open problem regarding the existence of a 2-string solution on S2. Furthermore, we prove that there are no symmetric solutions realizing N strings superimposed at a single point. Such a result implies, in particular, that there is no symmetric 1-string solution on S2 and is the only known non-existence theorem for cosmic strings confined on a compact surface. The symmetry of the underlying system enables us to work on a nonlinear ordinary differential equation subject to some prescribed boundary data at t = ±00. A shooting method is employed as an analytic tool in the study of the existence problem.

Original languageEnglish (US)
Pages (from-to)581-591
Number of pages11
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume453
Issue number1958
StatePublished - 1997

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Cosmic Strings
Criticality
strings
Strings
Ordinary differential equations
Winding number
Shooting Method
Symmetric Solution
Poles
Nonlinear Ordinary Differential Equations
Higgs
Nonexistence
Pole
Open Problems
Symmetry
Imply
differential equations
poles
theorems
Theorem

ASJC Scopus subject areas

  • General

Cite this

Static cosmic strings on S2 and criticality. / Yang, Yisong.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 453, No. 1958, 1997, p. 581-591.

Research output: Contribution to journalArticle

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