TY - JOUR

T1 - Topological solitons in the Weinberg-Salam theory

AU - Yang, Yisong

N1 - Funding Information:
The purpose of this paper is to present a fairly complete existence theory for the vortex-like solutions, in the critical Bogomol'nyi phase, of the classical Weinberg-Salam model (see the collected works edited by Lai\[17\]) and its two-Higgs-doublet extension unifying the electromagnetic and weak interactions. Solutions of such a nature give rise to multi-centered physical force concentrations which may be viewed as a many-particle system realized in two dimensions known as vortices \[11,12,22,25-27\]. These vortices are characterized by their local winding numbers or vortex charges and are topologically or energetically stable. In the ideal situations, vortices localize energy distributions and behave like classical solitons in interactions. In the context of cosmology, these topological solitons, known as cosmic strings \[5,7,9,10,15,16,19,33,34,36,37\], can also generate curvature fluctuations, apart * Supported in part by the National Science Foundation under grant DMS-9400243. I E-mail: yyang@math.poly.edu.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=4243950024&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243950024&partnerID=8YFLogxK

U2 - 10.1016/S0167-2789(96)00212-6

DO - 10.1016/S0167-2789(96)00212-6

M3 - Article

AN - SCOPUS:4243950024

SN - 0167-2789

VL - 101

SP - 55

EP - 94

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 1-2

ER -