Conformal nets and local field theory
arXiv:0912.5307
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 μ-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.
12 pages. Restricted loop group examples to the special unitary case; added references concerning finiteness for loop group nets; added examples of defects