### Abstract

In this paper we consider the bosonic sector of the electroweak theory. It has been shown in the work of Ambjorn and Olesen that when the Higgs mass equals to the mass of the Z boson, the model in two dimensions subject to the 't Hooft periodic boundary condition may be reduced to a Bogomol'nyi system and that the solutions of the system are vortices in a "dual superconductor". We shall prove using a constrained variational reformulation of the problem the existence of such vortices. Our conditions for the existence of solutions are necessary and sufficient when the vortex number N=1,2.

Original language | English (US) |
---|---|

Pages (from-to) | 1-16 |

Number of pages | 16 |

Journal | Communications in Mathematical Physics |

Volume | 144 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1992 |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

**On multivortices in the electroweak theory I : Existence of periodic solutions.** / Spruck, Joel; Yang, Yisong.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 144, no. 1, pp. 1-16. https://doi.org/10.1007/BF02099188

}

TY - JOUR

T1 - On multivortices in the electroweak theory I

T2 - Existence of periodic solutions

AU - Spruck, Joel

AU - Yang, Yisong

PY - 1992/2

Y1 - 1992/2

N2 - In this paper we consider the bosonic sector of the electroweak theory. It has been shown in the work of Ambjorn and Olesen that when the Higgs mass equals to the mass of the Z boson, the model in two dimensions subject to the 't Hooft periodic boundary condition may be reduced to a Bogomol'nyi system and that the solutions of the system are vortices in a "dual superconductor". We shall prove using a constrained variational reformulation of the problem the existence of such vortices. Our conditions for the existence of solutions are necessary and sufficient when the vortex number N=1,2.

AB - In this paper we consider the bosonic sector of the electroweak theory. It has been shown in the work of Ambjorn and Olesen that when the Higgs mass equals to the mass of the Z boson, the model in two dimensions subject to the 't Hooft periodic boundary condition may be reduced to a Bogomol'nyi system and that the solutions of the system are vortices in a "dual superconductor". We shall prove using a constrained variational reformulation of the problem the existence of such vortices. Our conditions for the existence of solutions are necessary and sufficient when the vortex number N=1,2.

UR - http://www.scopus.com/inward/record.url?scp=0001362245&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001362245&partnerID=8YFLogxK

U2 - 10.1007/BF02099188

DO - 10.1007/BF02099188

M3 - Article

AN - SCOPUS:0001362245

VL - 144

SP - 1

EP - 16

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -