Chern–Simons theory
For example, when Σ is a 2-sphere, this Hilbert space is one-dimensional and so there is only one state. When Σ is a 2-torus the states correspond to the integrable representations of the affine Lie algebra corresponding to g at level k. Characterizations of the conformal blocks at higher genera are not necessary for Witten's solution of Chern–Simons theory.