Conformal blocks from Wilson lines with loop corrections

TL;DR

This paper develops a Wilson line network approach in Chern-Simons theory to compute Virasoro and W$_N$ conformal blocks at large central charge, including loop corrections and regularization methods.

Contribution

It generalizes previous regularization techniques to handle more operators and applies the method to compute various conformal blocks for W$_3$ and W$_2$ models, including heavy-light and light-light cases.

Findings

Successfully computed W$_3$ identity block with loop corrections.

Derived light-light and heavy-light conformal blocks using Wilson lines.

Validated results against known conformal block calculations.

Abstract

We compute the conformal blocks of the Virasoro minimal model or its W$_N$ extension with large central charge from Wilson line networks in a Chern-Simons theory including loop corrections. In our previous work, we offered a prescription to regularize divergences from loops attached to Wilson lines. In this paper, we generalize our method with the prescription by dealing with more general operators for $N=3$ and apply it to the identity W$_3$ block. We further compute general light-light blocks and heavy-light correlators for $N=2$ with the Wilson line method and compare the results with known ones obtained using a different prescription. We briefly discuss general W$_3$ blocks.