Khovanov-Rozansky Homology and Topological Strings

Details Khovanov-Rozansky Homology and Topological Strings Khovanov-Rozansky Homology and Topological Strings

2004-12-20

arxiv.org/abs/hep-th/0412243v3

Lett.Math.Phys. 74 (2005) 53-74

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 2 figures, harvmac; minor corrections, references added

Scientific paper

10.1007/s11005-005-0008-8

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.

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