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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. doi:10.1016/S0550-3213(02)00620-X.

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We give a worldsheet proof of the equivalence between the U(N) Chern–Simons gauge theory on S³ 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.

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Ooguri, Hirosi0000-0001-6021-3778
Additional Information:© 2002 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 H.O. was supported in part by DOE grant DE-FG03-92-ER40701. The research of C.V. was supported in part by NSF grants PHY-9802709 and DMS-0074329.
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Department of Energy (DOE)DE-FG03-92-ER40701
Subject Keywords:2-dimensional black-hole; topological strings; invariants; model; amplitudes; manifolds; gravity; spaces
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Issue or Number:1-2
Record Number:CaltechAUTHORS:OOGnpb02
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Official Citation:Hirosi Ooguri, Cumrun Vafa, Worldsheet derivation of a large N duality, Nuclear Physics B, Volume 641, Issues 1–2, 2002, Pages 3-34, ISSN 0550-3213, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1631
Deposited By: Tony Diaz
Deposited On:09 Feb 2006
Last Modified:08 Nov 2021 19:11

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