Level-rank duality of knot and link invariants

Abstract

A number of results for the level-rank duality of $G(N{)}_K$ $\leftrightarrow$ $G(K{)}_N$ Chern-Simons theory are summarized, with emphasis on the applications to knot and link invariants. Explicit examples for $SU(2{)}_K$ $\leftrightarrow$ $SU(K{)}_2$ illustrate general results. A criterion to distinguish torus knots and links from hyperbolic knots and links, based on tables constructed by Kaul for one and two strand invariants, is presented. Possible symmetries of hyperbolic knot and link invariants are discussed. The level-rank duality of torus knot and link invariants of minimal models is examined

arXiv commentv3: added section on invariants for level -rank dual of minimal models and additional references

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Cited by in corpus (1)

• Topological phase, spin Chern-Simons theory and level rank duality on lens space