Topological solitons in the Weinberg-Salam theory

Research output: Contribution to journalArticle

Abstract

We establish the existence of multivortices arising in the self-dual phase of the standard model of Weinberg-Salam, and its two-Higgs-doublet extension, in the unified theory of electromagnetic and weak interactions. For the standard model, we prove the existence of solutions in a periodic lattice domain and study the effect of the gravitational coupling. We find an important connection of these self-dual vortices and the cosmological constant problem: the cosmological constant Λ may be written explicitly in terms of several fundamental parameters in electroweak theory and the two-dimensional surface on which the vortices reside becomes noncomplete. We then prove that such a gravitational background leads to the existence of finite-energy vortices on the full plane with a non-Abelian nature. For the extended electroweak model with two Higgs doublets, we solve the self-dual equations completely. For the periodic case, we prove an existence and uniqueness theorem under a necessary and sufficient condition. This result reveals some exact restrictions to the vortex charges. For the problem on the entire plane, we obtain existence, uniqueness, sharp decay estimates, and quantized fluxes.

Original languageEnglish (US)
Pages (from-to)55-94
Number of pages40
JournalPhysica D: Nonlinear Phenomena
Volume101
Issue number1-2
StatePublished - 1997

Fingerprint

Solitons
Vortex
Vortex flow
solitary waves
vortices
Cosmological Constant
Higgs
Standard Model
existence theorems
uniqueness theorem
electroweak model
Existence-uniqueness
Decay Estimates
Existence and Uniqueness Theorem
electromagnetic interactions
uniqueness
Existence of Solutions
constrictions
Charge
Entire

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Topological solitons in the Weinberg-Salam theory. / Yang, Yisong.

In: Physica D: Nonlinear Phenomena, Vol. 101, No. 1-2, 1997, p. 55-94.

Research output: Contribution to journalArticle

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