Knot Invariants and Topological Strings

Abstract

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.

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

Cited by in corpus (266)

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• Holomorphic Blocks in Three Dimensions
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• Deep Learning the Hyperbolic Volume of a Knot
• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
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• Chern-Simons Invariants of Torus Links
• Introduction to Khovanov Homologies. III. A new and simple tensor-algebra construction of Khovanov-Rozansky invariants
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