

Preprint 13/2004
Dynamics of ℂℙ1 lumps on a cylinder
Nuno Miguel Romao
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Submission date: 01. Apr. 2004
Pages: 37
published in: Journal of geometry and physics, 54 (2005) 1, p. 42-76
DOI number (of the published article): 10.1016/j.geomphys.2004.08.002
Bibtex
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Abstract:
The slow dynamics of topological solitons in the
-model, known as lumps, can be approximated by the geodesic
flow of the
metric on certain moduli spaces of holomorphic maps.
In the present work, we consider the dynamics of lumps on an
infinite flat cylinder, and we show that in this case the approximation can
be formulated naturally in terms of regular Kähler metrics.
We prove that these metrics are incomplete exactly in the multilump
(interacting) case. The metric for two-lumps can be computed in closed
form on certain totally geodesic submanifolds in terms of elliptic
integrals; particular geodesics are determined and discussed in terms of
the dynamics of interacting lumps.