Knot Invariants and Topological Strings

Details Knot Invariants and Topological Strings Knot Invariants and Topological Strings

1999-12-14

arxiv.org/abs/hep-th/9912123v3

Nucl.Phys.B577:419-438,2000

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, harvmac, 3 figures; An error in the Schwinger computation in two dimensions corrected; references added

Scientific paper

10.1016/S0550-3213(00)00118-8

We find further evidence for the conjecture relating large N Chern-Simons theory on S^3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of a simple knot on S^3 (for any representation) agrees to all orders in N with the corresponding quantity on the topological string side. For a general knot, we find a reformulation of the knot invariant in terms of new integral invariants, which capture the spectrum (and spin) of M2 branes ending on M5 branes embedded in the resolved conifold geometry. We also find an intriguing link between knot invariants and superpotential terms generated by worldsheet instantons in N=1 supersymmetric theories in 4 dimensions.

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