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Khovanov-Rozansky Homology and Topological Strings

Gukov, Sergei and Schwarz, Albert and Vafa, Cumrun (2005) Khovanov-Rozansky Homology and Topological Strings. Letters in Mathematical Physics, 74 (1). pp. 53-74. ISSN 0377-9017 . https://resolver.caltech.edu/CaltechAUTHORS:20160511-085302183

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Abstract

We conjecture a relation between the sl(N) knot homology, recently introduced by Khovanov and Rozansky, and the spectrum of BPS states captured by open topological strings. This conjecture leads to new regularities among the sl(N) knot homology groups and suggests that they can be interpreted directly in topological string theory. We use this approach in various examples to predict the sl(N) knot homology groups for all values of N. We verify that our predictions pass some non-trivial checks.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s11005-005-0008-8DOIArticle
http://link.springer.com/article/10.1007/s11005-005-0008-8PublisherArticle
http://arxiv.org/abs/hep-th/0412243arXivDiscussion Paper
Additional Information:© Springer 2005. Received: 21 March 2005. Dedicated to the memory of F.A. Berezin. We would like to thank D. Bar-Natan, R. Dijkgraaf, M. Gross, K. Intriligator, A. Kapustin, M. Khovanov, A. Klemm, M. Mariño, H. Ooguri, J. Roberts and D. Thurston for useful discussions. S.G. would also like to thank the Caltech Particle Theory Group for kind hospitality. The work of A.S. is supported by NSF grant DMS-0204927. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. S.G. is also supported in part by RFBR grant 04-02-16880. The work of C.V. is supported in part by NSF grants PHY-0244821 and DMS-0244464.
Funders:
Funding AgencyGrant Number
NSFDMS-0204927
Russian Foundation for Basic Research04-02-16880
NSFPHY-0244821
NSFDMS-0244464
Clay Mathematics InstituteUNSPECIFIED
Subject Keywords:knots, quantum group invariants, knot homology, topological strings, BPS states
Issue or Number:1
Classification Code:MSC (2000):57M25, 57M27, 18G60, 18E30, 14J32, 14N35, 81T30, 81T45.
Record Number:CaltechAUTHORS:20160511-085302183
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160511-085302183
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66974
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:11 May 2016 16:48
Last Modified:03 Oct 2019 10:01

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