Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representation theory in chiral conformal field theory: from fields to
  observables   This article develops new techniques for understanding the relationship
between the three different mathematical formulations of two-dimensional chiral
conformal field theory: conformal nets (axiomatizing local observables), vertex
operator algebras (axiomatizing fields), and Segal CFTs. It builds upon
previous work which introduced a geometric interpolation procedure for
constructing conformal nets from VOAs via Segal CFT, simultaneously relating
all three frameworks. In this article, we extend this construction to study the
relationship between the representation theory of conformal nets and the
representation theory of vertex operator algebras. We define a correspondence
between representations in the two contexts, and show how to construct
representations of conformal nets from VOAs. We also show that this
correspondence is rich enough to relate the respective 'fusion product'
theories for conformal nets and VOAs, by constructing local intertwiners (in
the sense of conformal nets) from intertwining operators (in the sense of
VOAs). We use these techniques to show that all WZW conformal nets can be
constructed using our geometric interpolation procedure.

36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys