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.
