Mathematical theory of self-dual cosmic strings: Existence and obstructions

Research output: Contribution to journalArticle

Abstract

This is a survey article concerning some recent mathematical results for the static selfdual cosmic-string solutions in the Abelian Higgs model and in the Weinberg-Salam standard model unifying electromagnetic and weak interactions, both coupled with gravity through the Einstein equations. For the Abelian Higgs strings there is a nearly complete picture. If the Riemann surface M on which the strings reside is compact, it can be shown that M must be S2 up to topological equivalence and there are only countably many values of the Higgs vacuum states for strings to exist. When M is noncompact and conformally a plane there are exact obstructions to the finiteness of energies and geodesic completeness of solutions. For the Weinberg-Salam strings, much is to be achieved. It Can be shown in this case that self-dual strings generated from W and Higgs condensation lead to an explicit formula for a positive cosmological constant and the gravitational metric is always noncomplete. This feature leads to the properties that the metric decays sufficiently rapidly at infinity and there exist non-Abelian electroweak strings of finite energies. It is established that for any integer N there are always suitable ranges of the electroweak parameters to allow the existence of W- and Higgs-condensed N-vortex solutions of finite energies.

Original languageEnglish (US)
Pages (from-to)203-227
Number of pages25
JournalInternational Journal of Modern Physics A
Volume11
Issue number2
StatePublished - 1996

Fingerprint

Cosmic Strings
Obstruction
Higgs
strings
Strings
Energy
Topological Equivalence
Metric
Einstein Equations
Cosmological Constant
Finiteness
Condensation
Riemann Surface
electromagnetic interactions
completeness
Geodesic
Einstein equations
Standard Model
Vortex
Explicit Formula

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Nuclear and High Energy Physics

Cite this

Mathematical theory of self-dual cosmic strings : Existence and obstructions. / Yang, Yisong.

In: International Journal of Modern Physics A, Vol. 11, No. 2, 1996, p. 203-227.

Research output: Contribution to journalArticle

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