Additivity, Haag duality, and non-invertible symmetries
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911328609763328 |
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| author | Shao, Shu-Heng Sorce, Jonathan Srivastava, Manu |
| author_facet | Shao, Shu-Heng Sorce, Jonathan Srivastava, Manu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Additivity, Haag duality, and non-invertible symmetries Shao, Shu-Heng Sorce, Jonathan Srivastava, Manu High Energy Physics - Theory Strongly Correlated Electrons Operator Algebras Quantum Physics 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. |
| title | Additivity, Haag duality, and non-invertible symmetries |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Operator Algebras Quantum Physics |
| url | https://arxiv.org/abs/2503.20863 |