Twistor Interpretation of Harmonic Spheres and Yang–Mills Fields

We consider the twistor descriptions of harmonic maps of the Riemann sphere into Kähler manifolds and Yang-Mills fields on four-dimensional Euclidean space. The motivation to study twistor interpretations of these objects comes from the harmonic spheres conjecture stating the existence of the biject...

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Bibliographic Details
Published in:Mathematics (Basel) 2015-03, Vol.3 (1), p.47-75
Main Author: Sergeev, Armen
Format: Article
Language:English
Subjects:
harmonic spheres
twistors
Yang-Mills fields
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Summary:We consider the twistor descriptions of harmonic maps of the Riemann sphere into Kähler manifolds and Yang-Mills fields on four-dimensional Euclidean space. The motivation to study twistor interpretations of these objects comes from the harmonic spheres conjecture stating the existence of the bijective correspondence between based harmonic spheres in the loop space \(\Omega G\) of a compact Lie group \(G\) and the moduli space of Yang-Mills \(G\)-fields on \(\mathbb R^4\).
ISSN:2227-7390
2227-7390
DOI:10.3390/math3010047