Khovanov-Rozansky Homology and Topological Strings

TL;DR

This paper proposes a conjectural link between Khovanov-Rozansky sl(N) knot homology and topological string BPS spectra, leading to new insights and predictions for knot homology groups across all N, verified through non-trivial checks.

Contribution

It introduces a novel conjecture connecting knot homology with topological string theory, enabling predictions of knot invariants for all N.

Findings

Predicted sl(N) knot homology groups for all N.

Identified new regularities in knot homology groups.

Validated predictions through non-trivial consistency checks.

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.