Speaker
Description
We briefly review $SL(2,\mathbb{C})$-Chern-Simons partition function $Z[\mathcal M]$ on a closed three-manifold $\mathcal{M}$ obtained from Dehn fillings on a link complement $\mathbf S^3\backslash {\mathcal{L}}$. We focus on links $\mathcal L$ which are connected sum of a knot $\mathcal K$ with a Hopf link $H$ ($\mathcal L= \mathcal{K}\# H$). Motivated by our earlier work on topological entanglement and the reduced density matrix $\sigma$ expression for such link complements, we wanted to determine a choice of Dehn filling so that ${\rm Tr}~ \sigma= Z[\mathcal M]$.
Using \textt{SnapPy}, we deduce a choice of the Dehn fillings which gives the
imaginary part of the leading order term in the perturbative expansion of $Z[\mathcal M]$ to be the hyperbolic volume of the knot $\mathcal K$. We have given explicit results for knots $\mathcal K= 4_1,5_2,6_1,6_2$ and $6_3$.
| Field of contribution | Theory |
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