Abstract
In previous work, we have shown that large field theory amplitudes, in Schwinger parametrized form, can be organized into integrals over the stringy moduli space . 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 () 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.
- Received 2 August 2005
DOI:https://doi.org/10.1103/PhysRevD.72.066008
©2005 American Physical Society