The Witten–Reshetikhin–Turaev correspondence for simplicial ribbon links

Let ${\mathfrak g}$ be as in Section 2, let $k\in\mathbb{N}$ satisfy $k>c_{\mathfrak g}$, and let $L$ be a colored simplicial ribbon link in $S^2\times S^1$ as in Theorem 1 or Theorem 2. Write $RT(L)$ for the Reshetikhin–Turaev invariant, with $L$ on the right-hand side regarded as a continuum ribbon link in $S^2\times S^1$. Witten–Reshetikhin–Turaev correspondence. One has

$$\operatorname{WLO}^{disc}_{norm}(L)=RT(L).$$

The conjecture asserts that the explicitly computed rigorous realization of the torus-gauge-fixed Chern–Simons path integral agrees with the corresponding Reshetikhin–Turaev invariant. The computation in the paper provides strong evidence, but the statement is presented as a conjecture rather than proved in full generality.