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

TL;DR

This paper constructs $rak{osp}(1|2)$ superconformal blocks in 3D Chern-Simons gravity using Wilson lines, providing explicit examples for light superprimary fields in the large central charge limit.

Contribution

It introduces a Wilson line approach to compute $rak{osp}(1|2)$ conformal blocks within the AdS/CFT framework for N=1 superconformal theories.

Findings

Explicit construction of two and three-point blocks on the sphere.

Calculation of one-point torus blocks for light superprimary fields.

Demonstration of conformal blocks via Wilson lines in Chern-Simons theory.

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.