Magnetic zero-modes, vortices and Cartan geometry

Calum Ross; Bernd Johannes Schroers

doi:10.1007/s11005-017-1023-2

Magnetic zero-modes, vortices and Cartan geometry

Calum Ross, Bernd Johannes Schroers^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

71 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 language	English
Pages (from-to)	1-35
Number of pages	35
Journal	Letters in Mathematical Physics
Early online date	7 Nov 2017
DOIs	https://doi.org/10.1007/s11005-017-1023-2
Publication status	E-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

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10.1007/s11005-017-1023-2

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AB - 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.

KW - Cartan geometry

KW - Dirac operator

KW - Magnetic zero-modes

KW - Vortex equations

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Magnetic zero-modes, vortices and Cartan geometry

Abstract

Keywords

ASJC Scopus subject areas

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