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

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.

References in corpus (4)

• A numerical algorithm for the explicit calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients
• Witten Diagrams for Torus Conformal Blocks
• Correlators in higher spin AdS_3 holography from Wilson lines with loop corrections
• Semiclassical torus blocks in the t-channel