(Anti-)instantons and the Atiyah-Hitchin manifold

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 the ory. In all these settings, (super)symmetries require the metric to be hype rkahler and have an SO(3) transitive isometry, which in the four-dimensiona l case essentially selects out the Atiyah-Hitchin manifold as the only such smooth manifold with the correct topology at infinity. In this paper, we a nalyze the exponentially small corrections to the asymptotic limit, and int erpret them as infinite series of instanton corrections in these various se ttings. Unexpectedly, the relevant configurations turn out to be bound stat es of n instantons and (n) over bar anti-instantons, with \n - (n) over bar \ = 0, 1 as required by charge conservation. We propose that the semi-class ical configurations relevant for the higher monopole moduli space are eucli dean open branes stretched between the monopoles.