Superconformal blocks from Wilson lines with loop corrections

TL;DR

This paper derives explicit formulas for $ ext{osp}(1|2)$ superconformal blocks with loop corrections using Wilson lines in Chern-Simons theory, advancing understanding of supersymmetric conformal structures at large central charge.

Contribution

It provides the first closed-form expressions for superconformal blocks including $1/c$ corrections, using Wilson line networks in $ ext{osp}(1|2)$ Chern-Simons theory.

Findings

Reproduced $1/c$ correction of conformal weight from Wilson lines.

Derived closed-form superconformal blocks with $1/c$ corrections.

Analyzed heavy operators related to supersymmetric conical spaces.

Abstract

We compute the $\mathcal{N}=1$ superconformal blocks from the networks of open Wilson lines in the $\text{osp}(1|2)$ Chern-Simons theory in the expansion of large central charge $c$. We first reproduce the $1/c$ correction of conformal weight from an open Wilson line by adopting the regularization prescription developed in our previous works. We then obtain the closed form expressions of superconformal blocks including $1/c$ corrections, which were not available before. We also examine heavy operators corresponding to supersymmetric conical spaces, and the geometry is quantized by utilizing the coadjoint orbits of the super Virasoro group. Superconformal blocks involving these operators are also examined.