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Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups. (English) Zbl 1387.58029
Summary: 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 Rényi 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 Rényi 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 Rényi entropy for these links shows a periodic structure in $$n$$ and vanishes whenever $$n$$ = 0 (mod p), where the integer 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 $$n$$.

##### MSC:
 58J28 Eta-invariants, Chern-Simons invariants 81T45 Topological field theories in quantum mechanics 81P40 Quantum coherence, entanglement, quantum correlations
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