Abelian gauge theory on Riemann surfaces and new topological invariants

Lesley Sibner, Robert Sibner, Yisong Yang

Research output: Contribution to journalArticle

Abstract

An Abelian gauge field theory framed on a complex line bundle L over a compact Riemann surface M is developed which allows the coexistence, simultaneously in the same model, of magnetic vortices and antivortices represented by the N zeros and P poles of a section of L. The quantized minimum energy E is given in terms of the first Chern class ci(L) and by a certain intersection number obtained from the multivortices. We show that E = 2ir(N + P). To realize such topological invariants as minimum energies, an existence and uniqueness theorem is established under the necessary and sufficient condition that |ci(L)| = \N -P\ < (total volume of M)/27r.

Original languageEnglish (US)
Pages (from-to)593-613
Number of pages21
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume456
Issue number1995
StatePublished - 2000

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Topological Invariants
Riemann Surface
Gauge Theory
Gages
gauge theory
Poles
Vortex flow
existence theorems
uniqueness theorem
Gauge Field Theories
Intersection number
Chern Classes
Existence and Uniqueness Theorem
Line Bundle
Energy
Coexistence
intersections
bundles
Pole
Vortex

Keywords

  • Characteristic classes
  • Complex line bundles
  • Leray-schauder theorem
  • Self-duality
  • Trudinger-moser inequality
  • Vortices

ASJC Scopus subject areas

  • General

Cite this

Abelian gauge theory on Riemann surfaces and new topological invariants. / Sibner, Lesley; Sibner, Robert; Yang, Yisong.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 456, No. 1995, 2000, p. 593-613.

Research output: Contribution to journalArticle

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