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تسجيل مستخدم جديدEntanglement on linked boundaries in Chern-Simons theory with generic gauge groups
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We study the entanglement for a state on linked torus boundaries in $3d$ Chern-Simons theory with a generic gauge group and present the asymptotic bounds of Renyi entropy at two different limits: (i) large Chern-Simons coupling $k$, and (ii) large rank $r$ of the gauge group. These results show that the Renyi entropies cannot diverge faster than $ln k$ and $ln r$, respectively. We focus on torus links $T(2,2n)$ with topological linking number $n$. The Renyi entropy for these links shows a periodic structure in $n$ and vanishes whenever $n = 0 text{ (mod } textsf{p})$, where the integer $textsf{p}$ is a function of coupling $k$ and rank $r$. We highlight that the refined Chern-Simons link invariants can remove such a periodic structure in $n$.
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We consider Chern-Simons theory for gauge group $G$ at level $k$ on 3-manifolds $M_n$ with boundary consisting of $n$ topologically linked tori. The Euclidean path integral on $M_n$ defines a quantum state on the boundary, in the $n$-fold tensor prod
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