Instanton strings and hyper-Kahler geometry

We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces, These N = (4, 4) superconformal field theories describe the near-horizon dynamics of the D1DS-brane system and are dual to string theory on AdS(3). We derive a precise map relating the moduli of the K3 type IIB string compactification to the moduli of these conformal field theories and the corresponding classical hyper-Kahler geometry. We conclude that in the absence of background gauge fields, the metric on the instanton moduli spaces degenerates exactly to the orbifold symmetric product of K3. Turning on a self-dual NS B-field deforms this symmetric product to a manifold that is diffeomorphic to the Hilbert scheme. We also comment on the mathematical applications of string duality to the global issues of deformations of hyper-Kahler manifolds, (C) 1999 Elsevier Science B.V.