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

Bao, J. ORCID: 0000-0002-9583-1696, Foda, O., He, Y-H. ORCID: 0000-0002-0787-8380 , Hirst, E. ORCID: 0000-0003-1699-4399, Read, J., Xiao, Y. & Yagi, F. (2021). Dessins d'enfants, Seiberg-Witten curves and conformal blocks. Journal of High Energy Physics, 2021(5), 65. doi: 10.1007/JHEP05(2021)065

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.

Publication Type: Article
Additional Information: This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
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