Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

The AdS/CFT correspondence asserts the equivalence of string theory on an anti-de-Sitter background geometry with four dimensional (super) Yang-Mills theories. In this talk we shall be primarily interested in relating the spectrum of string excitations to the anomalous scaling dimensions of composite operators (emerging from two point functions) in the gauge theory. Here considerable progress has been made in the last 3 years on both sides of the correspondence. After reviewing these recent developments we shall discuss a current project of ours of computing the AdS_5xS5 string spectrum in two limits in a light-cone formalism: The plane-wave (Penrose) and the flat space (large radius) limit and systematic perturbative corrections thereof.

We discuss a new twistor construction for anti-self-dual metrics on complex surfaces with first Betti number 1. We relate this result to the existence problem of locally conformally Kaehler metrics on compact surfaces.