Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915284397326336 |
|---|---|
| author | Fukusumi, Yoshiki Ji, Guangyue Yang, Bo |
| author_facet | Fukusumi, Yoshiki Ji, Guangyue Yang, Bo |
| contents | In this work, we revisit the operator-state correspondence in the Majorana conformal field theory (CFT) with emphasis on its semion representation. Whereas the semion representation (or $Z_{2}$ extension of the chiral Ising CFT) gives a concise ``abelian" (or invertible) representation in the level of fusion rule and quantum states, there exists subtlety when considering the chiral multipoint correlation function. In this sense, the operator-state correspondence in the semion sector of the fermionic theory inevitably contains difficulty coming from its anomalous conformal dimension $1/16$ as a $Z_{2}$ symmetry operator. By analyzing the asymptotic behaviors of the existing correlation functions, we propose a nontrivial correspondence between the chiral conformal blocks and bulk correlation functions containing both order and disorder fields. One can generalize this understanding to $Z_{N}$ models or fractional supersymmetric models (in which there exist long-standing open problems). We expect this may improve our understanding of the simple current extension of CFT which can appear commonly in the studies of topologically ordered systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15621 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders Fukusumi, Yoshiki Ji, Guangyue Yang, Bo High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons Mathematical Physics In this work, we revisit the operator-state correspondence in the Majorana conformal field theory (CFT) with emphasis on its semion representation. Whereas the semion representation (or $Z_{2}$ extension of the chiral Ising CFT) gives a concise ``abelian" (or invertible) representation in the level of fusion rule and quantum states, there exists subtlety when considering the chiral multipoint correlation function. In this sense, the operator-state correspondence in the semion sector of the fermionic theory inevitably contains difficulty coming from its anomalous conformal dimension $1/16$ as a $Z_{2}$ symmetry operator. By analyzing the asymptotic behaviors of the existing correlation functions, we propose a nontrivial correspondence between the chiral conformal blocks and bulk correlation functions containing both order and disorder fields. One can generalize this understanding to $Z_{N}$ models or fractional supersymmetric models (in which there exist long-standing open problems). We expect this may improve our understanding of the simple current extension of CFT which can appear commonly in the studies of topologically ordered systems. |
| title | Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2311.15621 |