Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-08-13
Commun.Math.Phys.186:585-599,1997
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, LaTeX2e, uses amsfonts and amsbsy packages
Scientific paper
10.1007/s002200050121
We use the HyperK\"{a}hler quotient of flat space to obtain some monopole moduli space metrics in explicit form. Using this new description, we discuss their topology, completeness and isometries. We construct the moduli space metrics in the limit when some monopoles become massless, which corresponds to non-maximal symmetry breaking of the gauge group. We also introduce a new family of HyperK"{a}hler metrics which, depending on the ``mass parameter'' being positive or negative, give rise to either the asymptotic metric on the moduli space of many SU(2) monopoles, or to previously unknown metrics. These new metrics are complete if one carries out the quotient of a non-zero level set of the moment map, but develop singularities when the zero-set is considered. These latter metrics are of relevance to the moduli spaces of vacua of three dimensional gauge theories for higher rank gauge groups. Finally, we make a few comments concerning the existence of closed or bound orbits on some of these manifolds and the integrability of the geodesic flow.
Gibbons Gary W.
Rychenkova Paulina
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