ADE triality via (non-)invertible symmetry gauging

2025/06/18 by Tanaka, Takahilo, Yu Nakayama, Nakayama, Yu · 1 citation
Biochemistry, Genetics and Molecular Biology · #FOS: Physical sciences #Gene expression and cancer classification #Genetics, Bioinformatics, and Biomedical Research #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2506.15158

openalex publication_date 2025/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is long known that A-series minimal models and D-series minimal models are exchanged by gauging the invertible ℤ₂ symmetry. More recently, it has been shown that A-series minimal models and E-series minimal models are exchanged by gauging a non-invertible symmetry. We complete the triality picture by showing that D-series minimal models and E-series minimal models are exchanged by gauging another non-invertible symmetry.

Citations

• ICTP lectures on (non-)invertible generalized symmetries
• Lectures on generalized symmetries
• Invertibility of Condensation Defects and Symmetries of 2 + 1d QFTs
• Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
• A-D-E Classification of Conformal Field Theories
• Module categories, weak Hopf algebras and modular invariants

Cited by

• Extending fusion rules with finite subgroups: For a general understanding of quotient or gauging

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• Discrete symmetries from hidden sectors
• Minimal Models RG flows: non-invertible symmetries & non-perturbative description
• Symmetry Problems in Low Energy Physics
• Fiducial Symmetry in Action
• Exceptionally simple exceptional models