1998/10/26 by Robbert Dijkgraaf, R. Dijkgraaf · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #hep-th #math.AG
paper · pdf · doi:10.1016/s0550-3213(98)00869-4
published as Nucl.Phys. B543 (1999) 545-571 · latex, 33 pages
arxiv created 1998/10/26 · openalex publication_date 1999/03/01 · arxiv updated 2009/11/30 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/01
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 D1-D5-brane system and are dual to string theory on AdS3. 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 hyperkaehler geometry. We conclude that, in the absense 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 hyperkaehler manifolds.