Abelian gauge theory on Riemann surfaces and new topological invariants

Lesley Sibner, Robert Sibner, Yisong Yang

Research output: Contribution to journalArticlepeer-review


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
Issue number1995
StatePublished - 2000


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

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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