Instantons, Monopoles and Toric HyperKähler Manifolds

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 hyperKähler 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 hyperKähler quotient is also presented. The effect of massless monopoles is briefly discussed.