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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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