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arXiv · hep-th/0605185

Topology and Energy of Time Dependent Unitons

Maciej Dunajski·Prim Plansangkate
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Abstract

We consider a class of time dependent finite energy multi-soliton solutions of the U(N) integrable chiral model in $(2+1)$ dimensions. The corresponding extended solutions of the associated linear problem have a pole with arbitrary multiplicity in the complex plane of the spectral parameter. Restrictions of these extended solutions to any spacelike plane in $\R^{2,1}$ have trivial monodromy and give rise to maps from a three sphere to U(N). We demonstrate that the total energy of each multi-soliton is quantised at the classical level and given by the third homotopy class of the extended solution. This is the first example of a topological mechanism explaining classical energy quantisation of moving solitons.

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Maciej Dunajski, Prim Plansangkate. 2006-11-26. Topology and Energy of Time Dependent Unitons. https://doi.org/10.1098/rspa.2006.1799

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