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

A preprint version of the article is available at arXiv.

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 \( \mathcal{N} \) = 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.

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Correspondence to Jiakang Bao.

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Dedicated to the memory of our dear friend, Professor Omar Foda, a gentleman and a scholar …

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Bao, J., Foda, O., He, YH. et al. Dessins d’enfants, Seiberg-Witten curves and conformal blocks. J. High Energ. Phys. 2021, 65 (2021). https://doi.org/10.1007/JHEP05(2021)065

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Keywords

  • Conformal Field Theory
  • Differential and Algebraic Geometry
  • Supersymmetric Gauge Theory