• Corpus ID: 238583698

Sewing and Propagation of Conformal Blocks

@inproceedings{Gui2021SewingAP,
  title={Sewing and Propagation of Conformal Blocks},
  author={Bin Gui},
  year={2021}
}

• Bin Gui
• Published 10 October 2021
• Mathematics

Propagation is a standard way of producing new conformal blocks from old ones that corresponds to the geometric procedure of adding new distinct points to a pointed compact Riemann surface. On the other hand, sewing conformal blocks corresponds to sewing compact Riemann surfaces. In this article, we clarify the relations between these two procedures. Most importantly, we show that ”sewing and propagation are commuting procedures”. More precisely: let φ be a conformal block associated to a vertex operator algebra V and a compact Riemann surface to be sewn, and let ≀ n φ be its n -times propagation. If the sewing r S φ converges, then r S ≀ n φ (the sewing of ≀ n φ ) converges to ≀ n r S φ (the n -times propagation of the sewing r S φ ). As an application, we can prove the convergence of sewing conformal blocks in certain important cases without assuming V to be CFT-type, C 2 -cofinite, or rational. We also provide a new method of explicitly constructing the permutation-twisted modules associated to the tensor product VOA V b k , originally due to [BDM02]. Our results are crucial for relating the (genus- 0 ) permutation-twisted V b k -conformal blocks and the untwisted V -conformal blocks (of possibly higher genera) [Gui21].