Topologically stratified energy minimizers in a product Abelian field theory
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 a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2015-09-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S055032131500262X |
| _version_ | 1818128780962562048 |
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| author | Xiaosen Han Yisong Yang |
| author_facet | Xiaosen Han Yisong Yang |
| author_sort | Xiaosen Han |
| collection | DOAJ |
| description | 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 value E=4π(N1+N2+P1+P2), given in terms of several topological invariants, measuring the total tension of the vortex-lines. |
| first_indexed | 2024-12-11T07:38:42Z |
| format | Article |
| id | doaj.art-924d93e9a824428cb96c40a92cbd1d6f |
| institution | Directory Open Access Journal |
| issn | 0550-3213 1873-1562 |
| language | English |
| last_indexed | 2024-12-11T07:38:42Z |
| publishDate | 2015-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-924d93e9a824428cb96c40a92cbd1d6f2022-12-22T01:15:39ZengElsevierNuclear Physics B0550-32131873-15622015-09-01898C60562610.1016/j.nuclphysb.2015.07.022Topologically stratified energy minimizers in a product Abelian field theoryXiaosen Han0Yisong Yang1Institute of Contemporary Mathematics, School of Mathematics and Statistics, Henan University, Kaifeng, Henan 475004, PR ChinaDepartment of Mathematics, Polytechnic School of Engineering, New York University, Brooklyn, NY 11201, USAWe 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 value E=4π(N1+N2+P1+P2), given in terms of several topological invariants, measuring the total tension of the vortex-lines.http://www.sciencedirect.com/science/article/pii/S055032131500262X |
| spellingShingle | Xiaosen Han Yisong Yang Topologically stratified energy minimizers in a product Abelian field theory Nuclear Physics B |
| title | Topologically stratified energy minimizers in a product Abelian field theory |
| title_full | Topologically stratified energy minimizers in a product Abelian field theory |
| title_fullStr | Topologically stratified energy minimizers in a product Abelian field theory |
| title_full_unstemmed | Topologically stratified energy minimizers in a product Abelian field theory |
| title_short | Topologically stratified energy minimizers in a product Abelian field theory |
| title_sort | topologically stratified energy minimizers in a product abelian field theory |
| url | http://www.sciencedirect.com/science/article/pii/S055032131500262X |
| work_keys_str_mv | AT xiaosenhan topologicallystratifiedenergyminimizersinaproductabelianfieldtheory AT yisongyang topologicallystratifiedenergyminimizersinaproductabelianfieldtheory |