Entanglement on linked boundaries in Chern Simons theory with generic gauge groups
A bstractWe 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.