Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups

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 (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.