Compactified Twistor Fibration and Topology of Ward Unitons
High Energy Physics - Theory
2016-03-23 v1 Differential Geometry
Exactly Solvable and Integrable Systems
Abstract
We use the compactified twistor correspondence for the (2+1)-dimensional integrable chiral model to prove a conjecture of Ward. In particular, we construct the correspondence space of a compactified twistor fibration and use it to prove that the second Chern numbers of the holomorphic vector bundles, corresponding to the uniton solutions of the integrable chiral model, equal the third homotopy classes of the restricted extended solutions of the unitons. Therefore we deduce that the total energy of a time-dependent uniton is proportional to the second Chern number.
Keywords
Cite
@article{arxiv.1504.06038,
title = {Compactified Twistor Fibration and Topology of Ward Unitons},
author = {Prim Plansangkate},
journal= {arXiv preprint arXiv:1504.06038},
year = {2016}
}