Connections between CFT and Topology via Knot Theory

R.J. Lawrence

Abstract: In this paper we shall discuss some of the isomorphisms established between the approach to conformal field theory on P^1 of Tsuchiya & Kanie MR89m:81166, and the topological construction of braid group representations of the author's thesis. These approaches both lead, in the simplest cases, to the one-variable Jones polynomial invariant of links, but can be generalised to give other invariants. The case of higher spin representations of sl(2) is discussed from the point of view of both approaches, and is used to re-interpret the well known connection with cabled links. The structure of the braid group representation obtained is also discussed in both the spin-half and higher spin cases, and is extended to give a representation of the category of tangles.

Keywords: knot theory, braid group, Jones polynomial, quantum groups, Yang-Baxter equation, conformal field theory, monodromy representation, Gauss-Manin connection, Knizhnik-Zamolodchikov equation

AMS subject classification: 20F36 32G34 57M25 81T40

Length: 10 pages

Reference: Lecture Notes in Physics 375 (1991) 245-254. MR1134160 (93f:20051) (review by Toshitake Kohno .)

Last updated on September 4th, 1996.