Low energy dynamics of a CP^1 lump on the sphere

TL;DR

This paper studies the low-energy behavior of a CP^1 lump on a spherical space by analyzing geodesic motion on the moduli space of static solutions, revealing its geometric structure and specific dynamical features.

Contribution

It explicitly computes the metric on the moduli space of static solutions for the CP^1 model on a sphere, including the structure of geodesic submanifolds and symmetry considerations.

Findings

Explicit metric functions derived for the moduli space

Identification of totally geodesic submanifolds

Qualitative description of lump dynamics on the sphere

Abstract

Low-energy dynamics in the unit-charge sector of the CP^1 model on spherical space (space-time S^2 x R) is treated in the approximation of geodesic motion on the moduli space of static solutions, a six-dimensional manifold with non-trivial topology and metric. The structure of the induced metric is restricted by consideration of the isometry group inherited from global symmetries of the full field theory. Evaluation of the metric is then reduced to finding five functions of one coordinate, which may be done explicitly. Some totally geodesic submanifolds are found and the qualitative features of motion on these described.