Dessins d’enfants, Seiberg-Witten curves and conformal blocks

DOI number:10.1007/JHEP05(2021)065

Journal:Journal of High Energy Physics

Abstract:We show how to map Grothendieck's dessins d'enfants to algebraic curves as Seiberg-Witten curves, then use the mirror map and the AGT map to obtain the corresponding 4d N=2 supersymmetric instanton partition functions and 2d Virasoro conformal blocks. We explicitly demonstrate the 6 trivalent dessins with 4 punctures on the sphere. We find that the parametrizations obtained from a dessin should be related by certain duality for gauge theories. Then we will discuss that some dessins could correspond to conformal blocks satisfying certain rules in different minimal models.

Note:The preprint version is available at https://arxiv.org/abs/2101.08843

Co-author:Jiakang Bao,Omar Foda,Yang-Hui He,Edward Hirst,James Read,Yan Xiao,Futoshi Yagi

Indexed by:SCI

Discipline:Science

Volume:05(2021)

Issue:065

Translation or Not:no

Date of Publication:2021-05-10

Included Journals:SCI

Links to published journals:https://doi.org/10.1007/JHEP05(2021)065