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Knot Invariants and Topological Strings

Ooguri, Hirosi and Vafa, Cumrun (2000) Knot Invariants and Topological Strings. Nuclear Physics B, 577 (3). pp. 419-438. ISSN 0550-3213. doi:10.1016/S0550-3213(00)00118-8.

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We find further evidence for the conjecture relating large N Chern-Simons theory on S^3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of a simple knot on S³ (for any representation) agrees to all orders in N with the corresponding quantity on the topological string side. For a general knot, we find a reformulation of the knot invariant in terms of new integral invariants, which capture the spectrum (and spin) of M2 branes ending on M5 branes embedded in the resolved conifold geometry. We also find an intriguing link between knot invariants and superpotential terms generated by worldsheet instantons in N=1 supersymmetric theories in 4 dimensions.

Item Type:Article
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URLURL TypeDescription Paper
Ooguri, Hirosi0000-0001-6021-3778
Additional Information:© 2000 Elsevier Science B.V. We are grateful to N. Berkovits, R. Gopakumar, K. Hori, S. Sinha, C. Taubes and T. Taylor for valuable discussions. H.O. would like to thank the theory group of Harvard University, where this work was initiated and completed. The research of H.O. was supported in part by NSF grant PHY-95-14797, DOE grant DE-AC03-76SF00098, and the Caltech Discovery Fund. The research of C.V. is supported by NSF Grant No. PHY-9218167.
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Department of Energy (DOE)DE-AC03-76SF00098
Caltech Discovery FundUNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20161219-085922769
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Official Citation:Hirosi Ooguri, Cumrun Vafa, Knot invariants and topological strings, Nuclear Physics B, Volume 577, Issue 3, 2000, Pages 419-438, ISSN 0550-3213, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72925
Deposited By: Tony Diaz
Deposited On:19 Dec 2016 17:27
Last Modified:11 Nov 2021 05:08

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