From free fields to AdS. III

Rajesh Gopakumar
Phys. Rev. D 72, 066008 – Published 19 September 2005

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 Mg,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 (σi=1/τi) 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.

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  • Received 2 August 2005

DOI:https://doi.org/10.1103/PhysRevD.72.066008

©2005 American Physical Society

Authors & Affiliations

Rajesh Gopakumar*

  • Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad, India 211019

  • *Electronic address: gopakumr@mri.ernet.in

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Issue

Vol. 72, Iss. 6 — 15 September 2005

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