Modular extension of topological orders from congruence representations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913296411525120 |
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| author | Seo, Donghae You, Minyoung Cho, Gil Young Kim, Hee-Cheol |
| author_facet | Seo, Donghae You, Minyoung Cho, Gil Young Kim, Hee-Cheol |
| contents | We present an efficient method to compute the modular extension of both fermionic topological orders and $\mathbb{Z}_2$-symmetric bosonic topological orders in two spatial dimensions, basing on congruence representations of $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups. To demonstrate the validity of our approach, we provide explicit calculations for topological orders with rank up to 10 for the fermionic cases and up to 6 for the bosonic cases. Along the way, we clarify the relation between fermionic rational conformal field theories, which live on the boundary of the corresponding fermionic topological orders, and modular extensions. In particular, we show that the $\mathrm{SL}_2(\mathbb{Z})$ representation of the R-R sector can be determined from the NS-NS sector using the modular extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00868 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Modular extension of topological orders from congruence representations Seo, Donghae You, Minyoung Cho, Gil Young Kim, Hee-Cheol Strongly Correlated Electrons High Energy Physics - Theory We present an efficient method to compute the modular extension of both fermionic topological orders and $\mathbb{Z}_2$-symmetric bosonic topological orders in two spatial dimensions, basing on congruence representations of $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups. To demonstrate the validity of our approach, we provide explicit calculations for topological orders with rank up to 10 for the fermionic cases and up to 6 for the bosonic cases. Along the way, we clarify the relation between fermionic rational conformal field theories, which live on the boundary of the corresponding fermionic topological orders, and modular extensions. In particular, we show that the $\mathrm{SL}_2(\mathbb{Z})$ representation of the R-R sector can be determined from the NS-NS sector using the modular extensions. |
| title | Modular extension of topological orders from congruence representations |
| topic | Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.00868 |