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Knots, links and branes at large \(N\). (English) Zbl 0990.81545
Summary: We consider Wilson loop observables for Chern-Simons theory at large \(N\) and its topological string dual and extend the previous checks for this duality to the case of links. We find an interesting structure involving representation/spin degeneracy of branes ending on branes which features in the large \(N\) dual description of Chern-Simons theory. This leads to a refinement of the integer invariants for links and knots. We illustrate our results with explicit computations on the Chern-Simons side.

MSC:
81T13 Yang-Mills and other gauge theories in quantum field theory
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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