Expansion for the solutions of the Bogomolny equations on the torus | Zendy

Antonio González-Arroyo | Zendy; Alberto Ramos | Zendy

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Expansion for the solutions of the Bogomolny equations on the torus

Author(s) -

Antonio González-Arroyo,

Alberto Ramos

Publication year - 2004

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2004/07/008

Subject(s) - torus , higgs boson , limit (mathematics) , convergence (economics) , plane (geometry) , abelian group , mathematics , position (finance) , geometry , mathematical analysis , physics , pure mathematics , quantum mechanics , economics , economic growth , finance

We show that the solutions of the Bogomolny equations for the Abelian Higgsmodel on a two-dimensional torus, can be expanded in powers of a quantityepsilon measuring the departure of the area from the critical area. This allowsa precise determination of the shape of the solutions for all magnetic fluxesand arbitrary position of the Higgs field zeroes. The expansion is carried outto 51 orders for a couple of representative cases, including the unit fluxcase. We analyse the behaviour of the expansion in the limit of large areas, inwhich case the solutions approach those on the plane. Our results suggestconvergence all the way up to infinite area.Comment: 26 pages, 8 figures, slightly revised version as published in JHE

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