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arXiv · 1711.06474

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

Siddharth Dwivedi·Vivek Kumar Singh·Saswati Dhara·P. Ramadevi·Yang Zhou·Lata Kh Joshi
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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 $n = 0 \text{ (mod } \textsf{p})$, where the integer $\textsf{p}$ 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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Siddharth Dwivedi, Vivek Kumar Singh, Saswati Dhara, P. Ramadevi, Yang Zhou, Lata Kh Joshi. 2018-03-01. Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups. https://doi.org/10.1007/jhep02(2018)163

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