THE HEISENBERG GROUP AND CONFORMAL FIELD THEORY

Abstract

A mathematical construction of the conformal field theory (CFT) associated to a compact torus, also called the ‘non-linear 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.