Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
High Energy Physics - Theory
2021-05-20 v3 Mathematical Physics
math.MP
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 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.
Keywords
Cite
@article{arxiv.2101.08843,
title = {Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks},
author = {Jiakang Bao and Omar Foda and Yang-Hui He and Edward Hirst and James Read and Yan Xiao and Futoshi Yagi},
journal= {arXiv preprint arXiv:2101.08843},
year = {2021}
}
Comments
55 pages; dedicated to the memory of Prof. Omar Foda; v3: minor corrections