The geometry and topology of the gauge theory/gravity correspondence

Abstract

The well studied AdS/CFT correspondence describes a duality between gauge theories and string theories. What is currently lacking is a dictionary translating gauge theory correlators in space-time to string theory correlators on a world-sheet. We investigate aspects of world-sheet correlators of closed string theories dual to large N SU(N) gauge theories following a prescription by Gopakumar. The prescription presents a concrete mapping of gauge theory correlators to string theory correlators. Gauge theory correlators are translated to string world-sheet correlators via a reparametrization by inverse Schwinger parameters and a mapping to the moduli space of Riemann surfaces (worldsheets) via a special class of quadratic differentials know as Strebel differentials.