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arXiv · 2503.20863

Additivity, Haag duality, and non-invertible symmetries

Shu-Heng Shao·Jonathan Sorce·Manu Srivastava
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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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Shu-Heng Shao, Jonathan Sorce, Manu Srivastava. 2025-03-26. Additivity, Haag duality, and non-invertible symmetries. https://doi.org/10.1007/jhep08(2025)009

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