  A mathematical construction of the conformal field theory (CFT) associated to
a compact torus, also called the "nonlinear Sigma-model" or "lattice-CFT", is
given. Underlying this approach to CFT is a unitary modular functor, the
construction of which follows from a "Quantization commutes with reduction"-
type of theorem for unitary quantizations of the moduli spaces of holomorphic
torus-bundles and actions of loop groups. This theorem in turn is a consequence
of general constructions in the category of affine symplectic manifolds and
their associated generalized Heisenberg groups.
