Wilson lines construction of osp(1|2) conformal blocks

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 osp(1|2) subalgebra of N=1 super-Virasoro algebra. We describe the construction of 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 osp(1|2). We study the correlation function for lower and upper components of the primary osp(1|2) doublets and show that the associated conformal blocks are obtained via Wilson line construction in Chern-Simons theory.