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Worldsheet derivation of a large N duality

Ooguri, Hirosi and Vafa, Cumrun (2002) Worldsheet derivation of a large N duality. Nuclear Physics B, 641 (1-2). pp. 3-34. ISSN 0550-3213. http://resolver.caltech.edu/CaltechAUTHORS:OOGnpb02

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Abstract

We give a worldsheet proof of the equivalence between the U(N) Chern-Simons gauge theory on S-3 and the topological closed string theory on the resolved conifold geometry. When the 't Hooft coupling of the gauge theory is small, the dual closed string worldsheet develops a new branch. We show that the fluctuations of the worldsheet into this branch effectively correspond to "holes" on the worldsheet, generating an open string sector. This leads to a microscopic description of how the 't Hooft expansion of gauge theory amplitudes is reproduced in the closed string computation. We find that the closed string amplitudes also contain terms which are not captured in the 't Hooft expansion but are present in the exact computation in the gauge theory amplitudes. These arise when the whole Riemann surface is in the new branch. We also discuss the cases with SO and Sp gauge groups.


Item Type:Article
Additional Information:Copyright © 2002. Published by Elsevier Science B.V. Received 4 July 2002; accepted 25 July 2002. Available online 13 August 2002. This article has been registered under preprint number hep-th/0205297. We thank M. Aganagic, R. Dijkgraaf, M. Douglas, R. Gopakumar, Y. Hashimoto, S. Katz, M. Marino, A. Strominger, N. Warner and E. Witten for valuable discussions. H.O. would like to thank the hospitality of the theory group at Harvard University. C.V. would like to thank the hospitality of the YITP at Stony Brook. The research of HO was supported in part by DOE grant DE-FG03-92-ER40701. The research of CV was supported in part by NSF grants PHY-9802709 and DMS-0074329. CALT-68-2386, CITUSC/02-019, HUTP-02/A018, hep-th/0205297
Subject Keywords:2-DIMENSIONAL BLACK-HOLE; TOPOLOGICAL STRINGS; INVARIANTS; MODEL; AMPLITUDES; MANIFOLDS; GRAVITY; SPACES
Record Number:CaltechAUTHORS:OOGnpb02
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:OOGnpb02
Alternative URL:http://dx.doi.org/10.1016/S0550-3213(02)00620-X
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1631
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Feb 2006
Last Modified:26 Dec 2012 08:45

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