ℤN duality and parafermions revisited

A bstract Given a two-dimensional bosonic theory with a non-anomalous ℤ 2 symmetry, the orbifolding and fermionization can be understood holographically using three-dimensional BF theory with level 2. From a Hamiltonian perspective, the information of dualities is encoded in a topological boundary s...

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Bibliographic Details
Published in:The journal of high energy physics 2023-11, Vol.2023 (11), p.206, Article 206
Main Authors: Duan, Zhihao, Jia, Qiang, Lee, Sungjay
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Eigenvectors
Elementary Particles
Hamiltonian functions
High energy physics
Operators
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Subgroups
Symmetry
Topology
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Summary:A bstract Given a two-dimensional bosonic theory with a non-anomalous ℤ 2 symmetry, the orbifolding and fermionization can be understood holographically using three-dimensional BF theory with level 2. From a Hamiltonian perspective, the information of dualities is encoded in a topological boundary state which is defined as an eigenstate of certain Wilson loop operators (anyons) in the bulk. We generalize this story to two-dimensional theories with non-anomalous ℤ N symmetry, focusing on parafermionization. We find the generic operators defining different topological boundary states including orbifolding and parafermionization with ℤ N or subgroups of ℤ N , and discuss their algebraic properties as well as the ℤ N duality web.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP11(2023)206