科研之友
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摘要
We demonstrate that the five vortex equations recently introduced by Manton arise as symmetry reductions of the anti-self-dual Yang-Mills equations in four dimensions. In particular the Jackiw-Pi vortex and the Ambjorn-Olesen vortex correspond to the gauge group SU(1, 1), and respectively the Euclidean or the SU(2) symmetry groups acting with two-dimensional orbits. We show how to obtain vortices with higher vortex numbers, by superposing vortex equations of different types. Finally we use the kinetic energy of the Yang-Mills theory in 4 + 1 dimensions to construct a metric on vortex moduli spaces. This metric is not positive-definite in cases of non-compact gauge groups.
- 出版日期2017-9-15
