Conformal blocks from Wilson lines with loop corrections

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.

53 pages, 6 figures, v2: an appendix analyzing a general W${}_3$ block added, v3: minor changes, published version

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• Supergroup Structure of Jackiw-Teitelboim Supergravity
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• Rectangular W-(super)algebras and their representations
• Scalar Blocks as Gravitational Wilson Networks
• A note on the Virasoro blocks at order $1/c$
• Superconformal blocks from Wilson lines with loop corrections
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• The Bulk-to-Boundary Propagator in Black Hole Microstate Backgrounds
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• Wilson lines construction of $\mathfrak{osp}(1|2)$ conformal blocks
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• Gravitational Wilson lines in AdS${}_3$