Conformal nets and local field theory

Details Conformal nets and local field theory Conformal nets and local field theory

2009-12-29

arxiv.org/abs/0912.5307v2

Mathematics

Algebraic Topology

12 pages. Restricted loop group examples to the special unitary case; added references concerning finiteness for loop group ne

Scientific paper

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.

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