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arXiv · 2203.10795

Unitary vertex algebras and Wightman conformal field theories

Christopher Raymond·Yoh Tanimoto·James E. Tener
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Abstract

We prove an equivalence between the following notions: (i) unitary M\"obius vertex algebras, and (ii) Wightman conformal field theories on the circle (with finite-dimensional conformal weight spaces) satisfying an additional condition that we call uniformly bounded order. Reading this equivalence in one direction, we obtain new analytic and operator-theoretic information about vertex operators. In the other direction we characterize OPEs of Wightman fields and show they satisfy the axioms of a vertex algebra. As an application we establish new results linking unitary vertex operator algebras with conformal nets.

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Christopher Raymond, Yoh Tanimoto, James E. Tener. 2022-03-21. Unitary vertex algebras and Wightman conformal field theories. https://doi.org/10.1007/s00220-022-04431-9

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