Additivity, Haag duality, and non-invertible symmetries

• URL: http://arxiv.org/abs/2503.20863v1
• Date: Wed, 26 Mar 2025 18:00:01 GMT
• Title: Additivity, Haag duality, and non-invertible symmetries
• Authors: Shu-Heng Shao, Jonathan Sorce, Manu Srivastava,
• Abstract summary: We study how "additivity" or "Haag duality" is violated in a 1+1D CFT or lattice model.<n>For the Verlinde symmetry of a bosonic diagonal RCFT, we find that additivity is violated whenever the symmetry algebra contains an invertible element.<n>We find similar phenomena for the Kramers-Wannier and Rep(D$_8$) non-invertible symmetries on spin chains.
• Score: 2.4578723416255754
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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$_8$) non-invertible symmetries on spin chains.

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