TY - JOUR

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

AU - Han, Xiaosen

AU - Yang, Yisong

N1 - Funding Information:
Han was partially supported by National Natural Science Foundation of China under Grant 11201118 and the Key Foundation for Henan colleges under Grant 15A110013 . Both authors were partially supported by National Natural Science Foundation of China under Grants 11471100 and 11471099 .
Publisher Copyright:
© 2015 The Authors.

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.

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U2 - 10.1016/j.nuclphysb.2015.07.022

DO - 10.1016/j.nuclphysb.2015.07.022

M3 - Article

AN - SCOPUS:84938272924

VL - 898

SP - 605

EP - 626

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -