Back to Search
Start Over
$\mathbb{Z}_N$ Duality and Parafermions Revisited
- Publication Year :
- 2023
-
Abstract
- Given a two-dimensional bosonic theory with a non-anomalous $\mathbb{Z}_2$ 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 $\mathbb{Z}_N$ symmetry, focusing on parafermionization. We find the generic operators defining different topological boundary states including orbifolding and parafermionization with $\mathbb{Z}_N$ or subgroups of $\mathbb{Z}_N$, and discuss their algebraic properties as well as the $\mathbb{Z}_N$ duality web.<br />Comment: 39 pages, 5 figures; references added; reference added, published version
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2309.01913
- Document Type :
- Working Paper