Conformal nets and local field theory
Abstract
We describe a coordinate-free notion of conformal nets as a mathematical model of conformal field theory. We define defects between conformal nets and introduce composition of defects, thereby providing a notion of morphism between conformal field theories. Altogether we characterize the algebraic structure of the collection of conformal nets as a symmetric monoidal tricategory. Dualizable objects of this tricategory correspond to conformal-net-valued 3-dimensional local topological quantum field theories. We prove that the dualizable conformal nets are the finite sums of irreducible nets with finite \mu-index. This classification provides a variety of 3-dimensional local field theories, including local field theories associated to central extensions of the loop groups of the special unitary groups.
Cite
@article{arxiv.0912.5307,
title = {Conformal nets and local field theory},
author = {Arthur Bartels and Christopher L. Douglas and André G. Henriques},
journal= {arXiv preprint arXiv:0912.5307},
year = {2010}
}
Comments
12 pages. Restricted loop group examples to the special unitary case; added references concerning finiteness for loop group nets; added examples of defects