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Conformal covariance and the split property
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We show that for a conformal local net of observables on the circle, the split property is automatic. Both full conformal covariance (i.e. diffeomorphism covariance) and the circle-setting play essential roles in this fact, while by previously constructed examples it was already known that even on the circle, M\"obius covariance does not imply the split property. On the other hand, here we also provide an example of a local conformal net living on the two-dimensional Minkowski space, which - although being diffeomorphism covariant - does not have the split property.
Forward citations
Cited by 2 Pith papers
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Integrating positive energy representations of the Virasoro algebra
Every unitary positive energy representation of the Virasoro algebra exponentiates to a holomorphic *-representation of the semigroup of annuli, and every representation of the Virasoro conformal net carries the same ...
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Rational and non-rational two-dimensional conformal field theories arising from lattices
Even lattices in an indefinite bilinear form classify two-dimensional conformal net extensions of Heisenberg nets under a discreteness assumption, with explicit rational and non-rational examples.
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