Chern–Simons theory
Witten gave a heuristic derivation of the Jones polynomial and its generalizations from Chern–Simons theory. The basic idea is simply that the vacuum expectation values of Wilson loops in Chern–Simons theory are link invariants because of the diffeomorphism-invariance of the theory. To calculate these expectation values, however, Witten needed to use the relation between Chern–Simons theory and a conformal field theory known as the Wess–Zumino–Witten model (or the WZW model).