Large-party limit of topological entanglement entropy in Chern-Simons theory
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arXiv
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| Natura: | Preprint |
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2026
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| author | Sain, Simran Dwivedi, Siddharth |
| author_facet | Sain, Simran Dwivedi, Siddharth |
| contents | We investigate the topological entanglement entropy of quantum states arising in the context of three-dimensional Chern-Simons theory with compact gauge group $G$ and Chern-Simons level $k$. We focus on the quantum states associated with the $T_{dm,dn}$ torus link complements, which is a $d$-party pure quantum state, and analyze its large-party limit, i.e., $d\to \infty$ limit. We show that the entanglement measures in this limit will receive contributions only from the Abelian anyons, and non-Abelian sectors are suppressed in the large-party limit. Consequently, the large-party limiting value of the entanglement entropy has an upper bound of $\ln |Z_G|$, where $|Z_G|$ is the order of the center of the group $G$. As an explicit example, we perform quantitative analysis for the simplest case of the SU(2) group and $T_{d,dn}$ torus link to obtain the large-party limit of the entanglement entropy. We further investigate the semiclassical ($k \to \infty$) limit of the entropies after taking the large-party limit for this particular example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00406 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large-party limit of topological entanglement entropy in Chern-Simons theory Sain, Simran Dwivedi, Siddharth High Energy Physics - Theory Mathematical Physics Quantum Physics We investigate the topological entanglement entropy of quantum states arising in the context of three-dimensional Chern-Simons theory with compact gauge group $G$ and Chern-Simons level $k$. We focus on the quantum states associated with the $T_{dm,dn}$ torus link complements, which is a $d$-party pure quantum state, and analyze its large-party limit, i.e., $d\to \infty$ limit. We show that the entanglement measures in this limit will receive contributions only from the Abelian anyons, and non-Abelian sectors are suppressed in the large-party limit. Consequently, the large-party limiting value of the entanglement entropy has an upper bound of $\ln |Z_G|$, where $|Z_G|$ is the order of the center of the group $G$. As an explicit example, we perform quantitative analysis for the simplest case of the SU(2) group and $T_{d,dn}$ torus link to obtain the large-party limit of the entanglement entropy. We further investigate the semiclassical ($k \to \infty$) limit of the entropies after taking the large-party limit for this particular example. |
| title | Large-party limit of topological entanglement entropy in Chern-Simons theory |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2601.00406 |