Exact solubility of Chern-Simons theory with compact simple gauge group

Abstract

We show that vacuum expectation values of Wilson loop operators in (2+1)-dimensional Chern-Simons theory satisfy algebraic equations. Interestingly enough, vacuum expectation values for unknotted Wilson loop operators in any representation of anu compact and simple group are exactly computed by solving the equations. So-called “skein relations”, which give us algebraic equations among vacuum expectations values of different Wilson loop operators, are constructed. In our formalism, quantum group symmetry appears naturally.