Magnetic zero-modes, vortices and Cartan geometry

Research output: Contribution to journalArticle

3 Citations (Scopus)
22 Downloads (Pure)

Abstract

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
DOIs
Publication statusE-pub ahead of print - 7 Nov 2017

Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'Magnetic zero-modes, vortices and Cartan geometry'. Together they form a unique fingerprint.

  • Cite this