Magnetic zero-modes, vortices and Cartan geometry

Calum Ross, Bernd Johannes Schroers*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
57 Downloads (Pure)


We exhibit a close relation between vortex configurations on the 2-sphere and magnetic zero-modes of the Dirac operator on (Formula presented.) which obey an additional nonlinear equation. We show that both are best understood in terms of the geometry induced on the 3-sphere via pull-back of the round geometry with bundle maps of the Hopf fibration. We use this viewpoint to deduce a manifestly smooth formula for square-integrable magnetic zero-modes in terms of two homogeneous polynomials in two complex variables.

Original languageEnglish
Pages (from-to)1-35
Number of pages35
JournalLetters in Mathematical Physics
Early online date7 Nov 2017
Publication statusE-pub ahead of print - 7 Nov 2017


  • Cartan geometry
  • Dirac operator
  • Magnetic zero-modes
  • Vortex equations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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