Local energy bounds and strong locality in chiral CFT

Carpi, Sebastiano and Tanimoto, Yoh and Weiner, Mihály (2022) Local energy bounds and strong locality in chiral CFT. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 390 (1). pp. 169-192. ISSN 0010-3616 (print); 1432-0916 (online)

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Abstract

A family of quantum fields is said to be strongly local if it generates a local netof von Neumann algebras. There are very limited methods of showingdirectlystronglocality of a quantum field. Among them, linear energy boundsare the most widelyused, yet a chiral conformal field of conformal weightd >2 cannot admit linear energybounds. We prove that if a chiral conformal field satisfies an energy bound of degree d−1, then it also satisfies a certain local version of the energybound, and this in turn implies strong locality. A central role in our proof is played by diffeomorphismsymmetry. As a concrete application, we show that the vertex operator algebra given by a unitary vacuum representation of theW3-algebra is strongly local. For central charge c >2, this yields a new conformal net. We further prove that these nets do notsatisfy strong additivity, and hence are not completely rational.

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