Representation theory in chiral conformal field theory: from fields to observables

Understand

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.