From free fields to AdS. III

Abstract

In previous work, we have shown that large N field theory amplitudes, in Schwinger parametrized form, can be organized into integrals over the stringy moduli space M_g,n×R₊ⁿ. Here we flesh this out into a concrete implementation of open-closed string duality. In particular, we propose that the closed string world sheet is reconstructed from the unique Strebel quadratic differential that can be associated to (the dual of) a field theory skeleton graph. We are led, in the process, to identify the inverse Schwinger proper times (σ_i=1/τ_i) with the lengths of edges of the critical graph of the Strebel differential. Kontsevich's matrix model derivation of the intersection numbers in moduli space provides a concrete example of this identification. It also exhibits how closed string correlators emerge very naturally from the Schwinger parameter integrals. Finally, to illustrate the utility of our approach to open-closed string duality, we outline a method by which a world sheet operator product expansion can be directly extracted from the field theory expressions. Limits of the Strebel differential for the four punctured sphere play a key role.