EXPLICIT CONSTRUCTION OF YANG-MILLS INSTANTONS ON ALE SPACES

We describe the explicit construction of Yang-Mills instantons on Asym ptotically Locally Euclidean (ALE) spaces, following the work of Kronh eimer and Nakajima. For multicenter ALE metrics, we determine the Abel ian instanton connections that are needed for the construction in the non-Abelian case, We compute the partition function of Maxwell theorie s on ALE manifolds and comment on the issue of electromagnetic duality . We discuss the topological characterization of the instanton bundles as well as the identification of their moduli spaces, We generalize t he 't Hooft ansatz to SU(2) instantons on ALE spaces and on other hype r-Kahler manifolds. Specializing to the Eguchi-Hanson gravitational ba ckground, we explicitly solve the ADHM equations for SU(2) gauge bundl es with second Chern class 1/2, 1 and 3/2.