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arXiv · 2409.08454

Non-unitary Wightman CFTs and non-unitary vertex algebras

Sebastiano Carpi·Christopher Raymond·Yoh Tanimoto·James E. Tener
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Abstract

We give an equivalence of categories between: (i) M\"obius vertex algebras which are equipped with a choice of generating family of quasiprimary vectors, and (ii) (not-necessarily-unitary) M\"obius-covariant Wightman conformal field theories on the unit circle. We do not impose any technical restrictions on the theories considered (such as finite-dimensional conformal weight spaces or simplicity), yielding the most general equivalence between these two axiomatizations of two-dimensional chiral conformal field theory. This provides new opportunities to study non-unitary vertex algebras using the lens of algebraic conformal field theory and operator algebras, which we demonstrate by establishing a non-unitary version of the Reeh-Schlieder theorem.

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Sebastiano Carpi, Christopher Raymond, Yoh Tanimoto, James E. Tener. 2024-09-13. Non-unitary Wightman CFTs and non-unitary vertex algebras. https://doi.org/10.1007/s00029-025-01063-4

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