Additivity, Haag duality, and non-invertible symmetries
arXiv:2503.20863 · doi:10.1007/JHEP08(2025)009
Abstract
The algebraic approach to quantum field theory focuses on the properties of local algebras, whereas the study of (possibly non-invertible) global symmetries emphasizes global aspects of the theory and spacetime. We study connections between these two perspectives by examining how either of two core algebraic properties -- "additivity" or "Haag duality" -- is violated in a 1+1D CFT or lattice model restricted to the symmetric sector of a general global symmetry. For the Verlinde symmetry of a bosonic diagonal RCFT, we find that additivity is violated whenever the symmetry algebra contains an invertible element, while Haag duality is violated whenever it contains a non-invertible element. We find similar phenomena for the Kramers-Wannier and Rep(D) non-invertible symmetries on spin chains.
22 pages, version published in JHEP
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