Implementation of conformal covariance by diffeomorphism symmetry

Abstract

Every locally normal representation of a local chiral conformal quantum theory is covariant with respect to global conformal transformations, if this theory is diffeomorphism covariant in its vacuum representation. The unitary, strongly continuous representation implementing conformal symmetry is constructed; it consists of operators which are inner in a global sense for the representation of the quantum theory. The construction is independent of positivity of energy and applies to all locally normal representations irrespective of their statistical dimensions (index).

arXiv comment11 pages,no figures

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• Representation theory in chiral conformal field theory: from fields to observables
• Fusion and positivity in chiral conformal field theory
• Solitons and nonsmooth diffeomorphisms in conformal nets
• Wightman fields for two-dimensional conformal field theories with pointed representation category
• Positive energy representations of Sobolev diffeomorphism groups of the circle
• Restricting positive energy representations of ${\mathrm{Diff}}^{+}(S^1)$ to the stabilizer of $n$ points
• Rotational KMS states and type I conformal nets
• Loop Groups and QNEC
• Bisognano-Wichmann property for rigid categorical extensions and non-local extensions of conformal nets
• Loop groups and noncommutative geometry