Chern-Simons Theory

Topological field theory: anyons, linking numbers & Wilson loops

Parameters

Linking #: 0
Phase: 0
Braids: 0
S_CS = k/4π ∫ A∧dA + ⅔A∧A∧A
Chern-Simons theory is purely topological — no metric needed. Wilson loops W(C) = Tr P exp(i∮A) are the observables.

Braiding two anyons of charge q at level k gives phase e^(2πiq²/k). This is the basis of topological quantum computing.