Wilson lines construction of $\mathfrak{osp}(1|2)$ conformal blocks

Abstract

We study N=1 superconformal theory in the context of AdS/CFT correspondence in the large central charge limit using Chern-Simons formulation of $3d$ gravity. In this limit conformal dimensions of a subclass of so-called light primary superfields remain finite and are governed by $\mathfrak{osp}(1|2)$ subalgebra of N=1 super-Virasoro algebra. We describe the construction of $\mathfrak{osp}(1|2)$ conformal blocks in terms of Wilson lines of the Chern-Simons $3d$ gravity. We consider examples of two and three-point blocks on the sphere and one-point torus blocks of light superprimary fields, which belong to finite-dimensional representations of $\mathfrak{osp}(1|2)$. We study the correlation function for lower and upper components of the primary $\mathfrak{osp}(1|2)$ doublets and show that the associated conformal blocks are obtained via Wilson line construction in Chern-Simons theory.

References in corpus (33)

• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Wilson Lines and Entanglement Entropy in Higher Spin Gravity
• Asymptotic Dynamics and Asymptotic Symmetries of Three-Dimensional Extended AdS Supergravity
• Semiclassical Virasoro Blocks from AdS${}_3$ Gravity
• Multipoint Conformal Blocks in the Comb Channel
• 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
• Representation theory of sl(2|1)
• From global to heavy-light: 5-point conformal blocks
• Holographic dual of the five-point conformal block
• Witten Diagrams for Torus Conformal Blocks
• Phases of scrambling in eigenstates
• Holographic Conformal Partial Waves as Gravitational Open Wilson Networks
• Holographic interpretation of 1-point toroidal block in the semiclassical limit
• Conformal blocks from Wilson lines with loop corrections
• Thermal Conformal Blocks
• Structure constants in the N=1 superoperator algebra
• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
• Holographic duals of large-c torus 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
• Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk
• Renormalization of gravitational Wilson lines
• Scalar Blocks as Gravitational Wilson Networks
• Correlation functions with fusion-channel multiplicity in W3 Toda field theory
• Holographic variables for CFT${}_2$ conformal blocks with heavy operators
• More on Wilson toroidal networks and torus blocks
• Geodesic description of Heavy-Light Virasoro blocks
• Multi-centered higher spin solutions from $W_N$ conformal blocks
• Semiclassical torus blocks in the t-channel
• On skew tau-functions in higher spin theory
• osp(1|2) Conformal Field Theory

Cited by in corpus (1)

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