Abstract
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.
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Dwivedi, S., Singh, V.K., Dhara, S. et al. Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups. J. High Energ. Phys. 2018, 163 (2018). https://doi.org/10.1007/JHEP02(2018)163
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DOI: https://doi.org/10.1007/JHEP02(2018)163