Topologically stratified energy minimizers in a product Abelian field theory

Xiaosen Han, Yisong Yang

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)605-626
Number of pages22
JournalNuclear Physics, Section B
Volume898
DOIs
StatePublished - Sep 1 2015

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vortices
products
energy
existence theorems
impurities
poles

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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

In: Nuclear Physics, Section B, Vol. 898, 01.09.2015, p. 605-626.

Research output: Contribution to journalArticle

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