### Abstract

We study a recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities. We first obtain a necessary and sufficient condition for the existence of a unique solution realizing such impurities in the form of multiple vortices. We next reformulate the theory into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from N<inf>s</inf> vortices and P<inf>s</inf> anti-vortices (s=1, 2) realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface S which states that a solution with prescribed N<inf>1</inf>, N<inf>2</inf> vortices and P<inf>1</inf>, P<inf>2</inf> anti-vortices of two designated species exists if and only if the inequalities|N1+N2-(P1+P2)|<|S|π,|N1+2N2-(P1+2P2)|<|S|π, hold simultaneously, which give bounds for the 'differences' of the vortex and anti-vortex numbers in terms of the total surface area of S. The minimum energy of these solutions is shown to assume the explicit valueE=4π(N1+N2+P1+P2), given in terms of several topological invariants, measuring the total tension of the vortex-lines.

Original language | English (US) |
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Pages (from-to) | 605-626 |

Number of pages | 22 |

Journal | Nuclear Physics, Section B |

Volume | 898 |

DOIs | |

State | Published - Sep 1 2015 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Topologically stratified energy minimizers in a product Abelian field theory.** / Han, Xiaosen; Yang, Yisong.

Research output: Contribution to journal › Article

*Nuclear Physics, Section B*, vol. 898, pp. 605-626. https://doi.org/10.1016/j.nuclphysb.2015.07.022

}

TY - JOUR

T1 - Topologically stratified energy minimizers in a product Abelian field theory

AU - Han, Xiaosen

AU - Yang, Yisong

PY - 2015/9/1

Y1 - 2015/9/1

N2 - We study a recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities. We first obtain a necessary and sufficient condition for the existence of a unique solution realizing such impurities in the form of multiple vortices. We next reformulate the theory into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from Ns vortices and Ps anti-vortices (s=1, 2) realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface S which states that a solution with prescribed N1, N2 vortices and P1, P2 anti-vortices of two designated species exists if and only if the inequalities|N1+N2-(P1+P2)|<|S|π,|N1+2N2-(P1+2P2)|<|S|π, hold simultaneously, which give bounds for the 'differences' of the vortex and anti-vortex numbers in terms of the total surface area of S. The minimum energy of these solutions is shown to assume the explicit valueE=4π(N1+N2+P1+P2), given in terms of several topological invariants, measuring the total tension of the vortex-lines.

AB - We study a recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities. We first obtain a necessary and sufficient condition for the existence of a unique solution realizing such impurities in the form of multiple vortices. We next reformulate the theory into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from Ns vortices and Ps anti-vortices (s=1, 2) realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface S which states that a solution with prescribed N1, N2 vortices and P1, P2 anti-vortices of two designated species exists if and only if the inequalities|N1+N2-(P1+P2)|<|S|π,|N1+2N2-(P1+2P2)|<|S|π, hold simultaneously, which give bounds for the 'differences' of the vortex and anti-vortex numbers in terms of the total surface area of S. The minimum energy of these solutions is shown to assume the explicit valueE=4π(N1+N2+P1+P2), given in terms of several topological invariants, measuring the total tension of the vortex-lines.

UR - http://www.scopus.com/inward/record.url?scp=84938272924&partnerID=8YFLogxK

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U2 - 10.1016/j.nuclphysb.2015.07.022

DO - 10.1016/j.nuclphysb.2015.07.022

M3 - Article

VL - 898

SP - 605

EP - 626

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -