Instantons, Monopoles and Toric HyperKaehler Manifolds

Details Instantons, Monopoles and Toric HyperKaehler Manifolds Instantons, Monopoles and Toric HyperKaehler Manifolds

1998-11-19

arxiv.org/abs/hep-th/9811179v1

Commun.Math.Phys. 212 (2000) 503-533

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, latex2e

Scientific paper

10.1007/s002200000223

In this paper, the metric on the moduli space of the k=1 SU(n) periodic instanton -or caloron- with arbitrary gauge holonomy at spatial infinity is explicitly constructed. The metric is toric hyperKaehler and of the form conjectured by Lee and Yi. The torus coordinates describe the residual U(1)^{n-1} gauge invariance and the temporal position of the caloron and can also be viewed as the phases of n monopoles that constitute the caloron. The (1,1,..,1) monopole is obtained as a limit of the caloron. The calculation is performed on the space of Nahm data, which is justified by proving the isometric property of the Nahm construction for the cases considered. An alternative construction using the hyperKaehler quotient is also presented. The effect of massless monopoles is briefly discussed.

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