Fivebranes and Knots

Details Fivebranes and Knots Fivebranes and Knots

2011-01-17

arxiv.org/abs/1101.3216v2

Physics

High Energy Physics

High Energy Physics - Theory

numerous small corrections from v. 1; 148 pp

Scientific paper

We develop an approach to Khovanov homology of knots via gauge theory (previous physics-based approches involved other descriptions of the relevant spaces of BPS states). The starting point is a system of D3-branes ending on an NS5-brane with a nonzero theta-angle. On the one hand, this system can be related to a Chern-Simons gauge theory on the boundary of the D3-brane worldvolume; on the other hand, it can be studied by standard techniques of $S$-duality and $T$-duality. Combining the two approaches leads to a new and manifestly invariant description of the Jones polynomial of knots, and its generalizations, and to a manifestly invariant description of Khovanov homology, in terms of certain elliptic partial differential equations in four and five dimensions.

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