Additivity, Haag duality, and non-invertible symmetries
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13130_2025_Article_26868.pdf
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606.96 KB
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Author(s)
Shao, Shu-Heng
Sorce, Jonathan
Srivastava, Manu
Date Issued
August 1, 2025
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Shao, SH., Sorce, J. & Srivastava, M. Additivity, Haag duality, and non-invertible symmetries. J. High Energ. Phys. 2025, 9 (2025).
Version
Final published version
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(D8) non-invertible symmetries on spin chains.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/JHEP08(2025)009
