Chern–Simons theory

Summary

Chern–Simons theory is a gauge theory on $3$-manifolds whose action is the Chern–Simons functional of a connection. The functional does not use a metric, so the quantum theory is a topological quantum field theory. Witten showed in 1989 that its expectation values of Wilson loops give the Jones polynomial. Its partition functions give new invariants of 3-manifolds, the quantum invariants. Its classical solutions are the flat connections, which link it with representations of fundamental groups and with the Casson invariant.