Symmetry, Symmetry Topological Field Theory and von Neumann Algebra
2025/07/23 by Jia, Qiang, Tian, Jiahua · 2 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2507.17103
Abstract
We study the additivity and Haag duality of the von Neumann algebra of a quantum field theory TF with 0-form (and the dual (d-2)-form) (non)-invertible global symmetry F. We analyze the symmetric (uncharged) sector von Neumann algebra of TF with the inclusion of bi-local and bi-twist operators in it. We establish the connection between the existence of these non-local operators in TF and certain properties of the Lagrangian algebra L of the extended operators in the corresponding symmetry topological field theory (SymTFT). We prove that additivity or Haag duality of the symmetric sector von Neumann algebra is violated when L satisfies specific criteria, thus generalizing the result of Shao, Sorce and Srivastava to arbitrary dimensions. We further demonstrate the SymTFT construction via concrete examples in two dimensions.
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