ar X iv : h ep - t h / 97 07 10 1 v 1 1 0 Ju l 1 99 7 Lump dynamics in the C P 1 model on the torus
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چکیده
The topology and geometry of the moduli space, M2, of degree 2 static solutions of the CP 1 model on a torus (spacetime T 2 × R) are studied. It is proved that M2 is homeomorphic to the left coset space G/G0 where G is a certain eight-dimensional noncompact Lie group and G0 is a discrete subgroup of order 4. Low energy two-lump dynamics is approximated by geodesic motion on M2 with respect to a metric g defined by the restriction to M2 of the kinetic energy functional of the model. This lump dynamics decouples into a trivial " centre of mass " motion and nontrivial relative motion on a reduced moduli space. It is proved that (M2, g) is geodesically incomplete and has only finite diameter. A low dimensional geodesic submanifold is identified and a full description of its geodesics obtained.
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تاریخ انتشار 1998