2025/12/01 by Yoshiki Fukusumi, Fukusumi, Yoshiki, Taishi Kawamoto +1 · 2 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2512.02139
openalex publication_date 2025/12/01 · openalex created_date 2025/12/04 · openalex updated_date 2026/07/28
We study fusion rings, or symmetry topological field theories (SymTFTs), which lie outside the non-negative integer matrix representation (NIM-rep), by combining knowledge from generalized symmetry and that from pseudo-Hermitian systems. By applying the Galois shuffle operation to the SymTFTs, we reconstruct fusion rings that correspond to nonlocal CFTs constructed from the corresponding local nonunitary CFTs by applying the similarity transformations. The resultant SymTFTs are outside of NIM-rep, whereas they are ring isomorphic to the NIM-rep of the corresponding local nonunitary CFTs. We study the consequences of this correspondence between the nonlocal unitary model and local nonunitary models. We demonstrate the correspondence between their classifications of massive or massless renormalization group flows and the discrepancies between their boundary or domain wall phenomena. Our work reveals a new connection between ring isomorphism and similarity transformations, providing the fundamental implications of ring-theoretic ideas in the context of symmetry in physics.