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arXiv · 2301.04575

Wilson lines construction of $\mathfrak{sl}_3$ toroidal conformal blocks

Vladimir Belavin·Pietro Oreglia·Juan Ramos Cabezas
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Abstract

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.

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Vladimir Belavin, Pietro Oreglia, Juan Ramos Cabezas. 2023-01-11. Wilson lines construction of $\mathfrak{sl}_3$ toroidal conformal blocks. https://doi.org/10.1016/j.nuclphysb.2023.116186

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