Gapped boundary of (4+1)d beyond-cohomology bosonic SPT phase
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_ | 1866910535640940544 |
|---|---|
| author | Yang, Xinping Cheng, Meng |
| author_facet | Yang, Xinping Cheng, Meng |
| contents | In this work we study gapped boundary states of $\mathbb{Z}_N$ bosonic symmetry-protected topological (SPT) phases in 4+1d, which are characterized by mixed $\mathbb{Z}_N$-gravity response, and the closely related phases protected by $C_N$ rotation symmetry. We show that if $N\notin \{2,4,8,16\}$, any symmetry-preserving boundary theory is necessarily gapless for the root SPT state. We then propose a (3+1)$d$ $\mathbb{Z}_2$ gauge theory coupled to fermionic matter as a candidate boundary theory for $N=2,4,8,16$, where the anomalous symmetry is implemented by invertible topological defects obtained from gauging (2+1)$d$ chiral topological superconductors. For the $C_N$ case, we present an explicit construction for the boundary states for $N=2,4,8,16$, and argue that the construction fails for other values of $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_00719 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gapped boundary of (4+1)d beyond-cohomology bosonic SPT phase Yang, Xinping Cheng, Meng Strongly Correlated Electrons High Energy Physics - Theory In this work we study gapped boundary states of $\mathbb{Z}_N$ bosonic symmetry-protected topological (SPT) phases in 4+1d, which are characterized by mixed $\mathbb{Z}_N$-gravity response, and the closely related phases protected by $C_N$ rotation symmetry. We show that if $N\notin \{2,4,8,16\}$, any symmetry-preserving boundary theory is necessarily gapless for the root SPT state. We then propose a (3+1)$d$ $\mathbb{Z}_2$ gauge theory coupled to fermionic matter as a candidate boundary theory for $N=2,4,8,16$, where the anomalous symmetry is implemented by invertible topological defects obtained from gauging (2+1)$d$ chiral topological superconductors. For the $C_N$ case, we present an explicit construction for the boundary states for $N=2,4,8,16$, and argue that the construction fails for other values of $N$. |
| title | Gapped boundary of (4+1)d beyond-cohomology bosonic SPT phase |
| topic | Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2303.00719 |