On the ADHM construction on ALE gravitational backgrounds

In this letter we report on the explicit construction of self-dual connections on Asymptotically Locally Euclidean spaces following the approach of Kronheimer and Nakajima. Restricting ourselves to the simplest case of an SU(2) connection with the lowest Chern class on the Eguchi-Hanson gravitational background, we study the wave operators for scalar, spinor and vector fields in the adjoint representation of the gauge group and verify that the metric on the moduli space coincides with the metric on the base manifold.