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 (24)

• Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Wilson Lines and Entanglement Entropy in Higher Spin Gravity
• Semiclassical Virasoro Blocks from AdS${}_3$ Gravity
• A numerical algorithm for the explicit calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients
• Entanglement Entropy and Higher Spin Holography in AdS${}_3$
• Monodromic vs geodesic computation of Virasoro classical conformal blocks
• Higher-point conformal blocks and entanglement entropy in heavy states
• From global to heavy-light: 5-point conformal blocks
• Witten Diagrams for Torus Conformal Blocks
• Holographic Conformal Partial Waves as Gravitational Open Wilson Networks
• Conformal blocks from Wilson lines with loop corrections
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• Thermal Conformal Blocks
• Correlators in higher spin AdS_3 holography from Wilson lines with loop corrections
• General Results for Higher Spin Wilson Lines and Entanglement in Vasiliev Theory
• Renormalization of gravitational Wilson lines
• Scalar Blocks as Gravitational Wilson Networks
• Correlation functions with fusion-channel multiplicity in W3 Toda field theory
• Multi-centered higher spin solutions from $W_N$ conformal blocks
• More on Wilson toroidal networks and torus blocks
• Semiclassical torus blocks in the t-channel
• On skew tau-functions in higher spin theory
• Wilson lines construction of $\mathfrak{osp}(1|2)$ conformal blocks