The Heisenberg group and conformal field theory
Mathematical Physics
2011-05-25 v3 math.MP
Abstract
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.
Cite
@article{arxiv.0706.4262,
title = {The Heisenberg group and conformal field theory},
author = {Hessel Posthuma},
journal= {arXiv preprint arXiv:0706.4262},
year = {2011}
}