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Mathematics 2015, 3(1), 47-75;

Twistor Interpretation of Harmonic Spheres and Yang–Mills Fields

Steklov Mathematical Institute, Gubkina 8,119991, Moscow, Russia
Academic Editor: Palle Jorgensen
Received: 24 January 2015 / Accepted: 4 March 2015 / Published: 16 March 2015
(This article belongs to the Special Issue Mathematical physics)
Full-Text   |   PDF [330 KB, uploaded 16 March 2015]


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 \(\mathbb R^4\). View Full-Text
Keywords: harmonic spheres; Yang-Mills fields; twistors harmonic spheres; Yang-Mills fields; twistors
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Sergeev, A. Twistor Interpretation of Harmonic Spheres and Yang–Mills Fields. Mathematics 2015, 3, 47-75.

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