Abstract
In the previous chapters, we analyzed the various schemes that have been proposed to catalog large numbers of conformal field theories, especially the rational ones with a finite number of primary fields. In this chapter, we will explore the most ambitious one, which is the use of Chern—Simons gauge theory [1] to classify conformal field theories. In the process, we will uncover a deep but unexpected relationship between conformal field theories and knot theory. Surprisingly, we will be able to use quantum field theory to generate new knot polynomials and analytic expressions for them. Knot theory, in turn, will be a tool by which we study conformal field theories and statistical mechanics, giving us a topological meaning to the Yang-Baxter relation.
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Kaku, M. (2000). Knot Theory and Quantum Groups. In: Strings, Conformal Fields, and M-Theory. Graduate Texts in Contemporary Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0503-6_8
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DOI: https://doi.org/10.1007/978-1-4612-0503-6_8
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