Abstract
Given a two-dimensional bosonic theory with a non-anomalous ℤ2 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 ℤN symmetry, focusing on parafermionization. We find the generic operators defining different topological boundary states including orbifolding and parafermionization with ℤN or subgroups of ℤN, and discuss their algebraic properties as well as the ℤN duality web.
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Acknowledgments
We would like to thank Chi-Ming Chang, Jin Chen and Kimyeong Lee for helpful discussions. We also thank Chi-Ming Chang for comments on the draft. ZD thanks Fudan University, Shanghai for hospitality where part of this project was carried out. The main result of this work was presented by QJ at the 4th National Workshop on Fields and Strings held in Nanjing, and QJ is grateful to the audience for feedback. ZD, QJ, and SL are supported by KIAS Grant PG076902, PG080802 and PG056502.
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Duan, Z., Jia, Q. & Lee, S. ℤN duality and parafermions revisited. J. High Energ. Phys. 2023, 206 (2023). https://doi.org/10.1007/JHEP11(2023)206
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DOI: https://doi.org/10.1007/JHEP11(2023)206