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From Free Fields to $AdS$ -- III | | Rajesh Gopakumar
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28 Apr 2005 | | Journal: | Phys.Rev. D72 (2005) 066008 | | Subject: | hep-th | | Affiliation: | Harish-Chandra Research Institute | | Abstract: | In previous work we have shown that large $N$ field theory amplitudes, in Schwinger parametrised form, can be organised into integrals over the stringy moduli space ${cal M}_{g,n} imes R_{+}^n$. Here we flesh this out into a concrete implementation of open-closed string duality. In particular, we propose that the closed string worldsheet 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 ($s_i={1over _i}$) 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 very naturally emerge 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 worldsheet OPE can be directly extracted from the field theory expressions. Limits of the Strebel differential for the four punctured sphere play a key role. | | Source: | arXiv, hep-th/0504229 | | Services: | Forum | Review | PDF | Favorites | |
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