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arXiv · 2507.20735

Every conformal net has an associated unitary VOA

André G. Henriques·James E. Tener
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Abstract

Unitary vertex operator algebras (VOAs) and conformal nets are the two most prominent mathematical axiomatizations of two-dimensional unitary chiral conformal field theories. They are conjectured to be equivalent, but a rigorous comparison has proven challenging. We resolve one direction of the conjecture by showing that every conformal net has an associated unitary VOA. We also show that every representation of a conformal net in which the generator of rotation acts with discrete spectrum and finite-dimensional eigenspaces yields a unitary module of the corresponding VOA. A talk describing our results is available at: https://www.youtube.com/watch?v=f_LhNSeiiaE .

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André G. Henriques, James E. Tener. 2025-07-28. Every conformal net has an associated unitary VOA. https://arxiv.org/abs/2507.20735

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