Wilson lines construction of sl3 toroidal conformal blocks

Abstract

We study W3 toroidal conformal blocks for degenerate primary fields in AdS/CFT context. In the large central charge limit W3 algebra reduces to sl3 algebra and sl3 blocks are defined as contributions to W3 blocks coming from the generators of sl3 subalgebra. We consider the construction of sl3 toroidal blocks in terms of Wilson lines operators of 3d Chern-Simons gravity in the thermal AdS3 space-time. According to the correspondence, degenerate primary fields are associated with Wilson lines operators acting in the corresponding finite-dimensional sl3 representations. We verify this dual construction for one-point toroidal block using sl3 tensor technique in the bulk theory and an algorithm based on AGT correspondence in the boundary CFT.