### Speaker

### Description

We study $\mathcal{W}_3$ toroidal conformal blocks for degenerate primary fields in AdS/CFT context.

In the large central charge limit $\mathcal{W}_3$ algebra reduces to $\mathfrak{sl}_3$ algebra and $\mathfrak{sl}_3$ blocks are defined as contributions to $\mathcal{W}_3$ blocks coming from the generators of $\mathfrak{sl}_3$ subalgebra.

We consider the construction of $\mathfrak{sl}_3$

toroidal blocks in terms of Wilson lines operators of $3d$ Chern-Simons gravity in the thermal AdS$_3$ space-time. According to the correspondence,

degenerate primary fields are associated with Wilson lines operators acting in the corresponding finite-dimensional $\mathfrak{sl}_3$ representations. We verify

this dual construction

for one-point toroidal block using

$\mathfrak{sl}_3$ tensor technique in the bulk theory and an algorithm based on AGT correspondence in the boundary CFT.