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- Title
Quantum operations on conformal nets.
- Authors
Bischoff, Marcel; Del Vecchio, Simone; Giorgetti, Luca
- Abstract
On a conformal net , one can consider collections of unital completely positive maps on each local algebra (I) , subject to natural compatibility, vacuum preserving and conformal covariance conditions. We call quantum operations on the subset of extreme such maps. The usual automorphisms of (the vacuum preserving invertible unital *-algebra morphisms) are examples of quantum operations, and we show that the fixed point subnet of under all quantum operations is the Virasoro net generated by the stress-energy tensor of . Furthermore, we show that every irreducible conformal subnet ℬ ⊂ is the fixed points under a subset of quantum operations. When ℬ ⊂ is discrete (or with finite Jones index), we show that the set of quantum operations on that leave ℬ elementwise fixed has naturally the structure of a compact (or finite) hypergroup, thus extending some results of [M. Bischoff, Generalized orbifold construction for conformal nets, Rev. Math. Phys. 29 (2017) 1750002]. Under the same assumptions, we provide a Galois correspondence between intermediate conformal nets and closed subhypergroups. In particular, we show that intermediate conformal nets are in one-to-one correspondence with intermediate subfactors, extending a result of Longo in the finite index/completely rational conformal net setting [R. Longo, Conformal subnets and intermediate subfactors, Comm. Math. Phys. 237 (2003) 7–30].
- Subjects
ORBIFOLDS; PETRI nets; ALGEBRAIC field theory; QUANTUM field theory; AUTOMORPHISMS
- Publication
Reviews in Mathematical Physics, 2023, Vol 35, Issue 4, p1
- ISSN
0129-055X
- Publication type
Article
- DOI
10.1142/S0129055X23500071