3-6 July 2023
Europe/Amsterdam timezone

Wilson lines construction of sl3 toroidal conformal blocks

5 Jul 2023, 09:30
20 Min Talk Participants Talks


Pietro OREGLIA (Ariel University)


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.

Primary authors

Pietro OREGLIA (Ariel University) Prof. Vladimir BELAVIN (Ariel University) Juan RAMOS CABEZAS (Ariel University)

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