Khovanov-Rozansky Homology and Topological Strings

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.

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

References in corpus (3)

• Matrix Factorizations And Mirror Symmetry: The Cubic Curve
• The Superpolynomial for Knot Homologies
• Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefolds

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