Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-05-17
JHEP 0007 (2000) 001
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, 5 figures
Scientific paper
10.1088/1126-6708/2000/07/001
The Atiyah-Hitchin manifold arises in many different contexts, ranging from its original occurrence as the moduli space of two SU(2) 't Hooft-Polyakov monopoles in 3+1 dimensions, to supersymmetric backgrounds of string theory. In all these settings, (super)symmetries require the metric to be hyperk\"ahler and have an SO(3) transitive isometry, which in the four-dimensional case essentially selects out the Atiyah-Hitchin manifold as the only such smooth manifold with the correct topology at infinity. In this paper, we analyze the exponentially small corrections to the asymptotic limit, and interpret them as infinite series of instanton corrections in these various settings. Unexpectedly, the relevant configurations turn out to be bound states of $n$ instantons and $\bar n$ anti-instantons, with $|n-\bar n|=0,1$ as required by charge conservation. We propose that the semi-classical configurations relevant for the higher monopole moduli space are Euclidean open branes stretched between the monopoles.
Hanany Amihay
Pioline Boris
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