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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2412.11486 |
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| _version_ | 1866909712537092096 |
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| author | Takahashi, Shunta |
| author_facet | Takahashi, Shunta |
| contents | Anyon condensation in wormhole geometries is investigated in the Virasoro TQFT (VTQFT) formulation, a proposed reformulation of 3d AdS quantum gravity. We first review some elementary techniques of VTQFT and summarize a gauging scheme for non-invertible symmetries referred to as anyon condensation. We then exhibit that anyon condensation is applicable to VTQFT even though the category of Wilson lines associated with it is not strictly a modular tensor category (MTC) due to the continuously infinite label $p\in\mathbb{R}_+$. More specifically, it is shown that the partition function of the wormhole factorizes upon condensing the so-called diagonal condensable anyon $\mathcal{A}=\int_{0}^{\infty}dp\,L_p\boxtimes\overline{L}_p$ in VTQFT. The resulting $2$d boundary theory is Liouville CFT by symmetry TFT construction, and to our knowledge, this is among the very few explicit computational examples of gauging \textit{continuous non-invertible} symmetries in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11486 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anyon Condensation in Virasoro TQFT: Wormhole Factorization Takahashi, Shunta High Energy Physics - Theory Strongly Correlated Electrons Anyon condensation in wormhole geometries is investigated in the Virasoro TQFT (VTQFT) formulation, a proposed reformulation of 3d AdS quantum gravity. We first review some elementary techniques of VTQFT and summarize a gauging scheme for non-invertible symmetries referred to as anyon condensation. We then exhibit that anyon condensation is applicable to VTQFT even though the category of Wilson lines associated with it is not strictly a modular tensor category (MTC) due to the continuously infinite label $p\in\mathbb{R}_+$. More specifically, it is shown that the partition function of the wormhole factorizes upon condensing the so-called diagonal condensable anyon $\mathcal{A}=\int_{0}^{\infty}dp\,L_p\boxtimes\overline{L}_p$ in VTQFT. The resulting $2$d boundary theory is Liouville CFT by symmetry TFT construction, and to our knowledge, this is among the very few explicit computational examples of gauging \textit{continuous non-invertible} symmetries in the literature. |
| title | Anyon Condensation in Virasoro TQFT: Wormhole Factorization |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2412.11486 |