Exploring topological entanglement through Dehn surgery

• URL: http://arxiv.org/abs/2402.07459v1
• Date: Mon, 12 Feb 2024 07:38:14 GMT
• Title: Exploring topological entanglement through Dehn surgery
• Authors: Aditya Dwivedi, Siddharth Dwivedi, Vivek Kumar Singh, Pichai Ramadevi, Bhabani Prasad Mandal
• Abstract summary: We compute the partition function of a closed 3-manifold obtained from Dehn fillings of the link complement. We have given explicit results for all hyperbolic knots $mathcalK$ up to six crossings.
• Score: 1.3328842853079743
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We compute the $\text{PSL}(2,\mathbb{C})$ Chern-Simons partition function of a closed 3-manifold obtained from Dehn fillings of the link complement $\mathbf S^3\backslash {\mathcal{L}}$, where $\mathcal{L}=\mathcal{K}# H$ is the connected sum of the knot $\mathcal {K}$ with the Hopf link $H$. Motivated by our earlier work on topological entanglement and the reduced density matrix $\sigma$ for such link complements, we wanted to determine a choice of Dehn filling so that the trace of the matrix $\sigma$ becomes equal to the $\text{PSL}(2,\mathbb{C})$ partition function of the closed 3-manifold. We use the SnapPy program and numerical techniques to show this equivalence up to the leading order. We have given explicit results for all hyperbolic knots $\mathcal{K}$ up to six crossings.

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