Dessins d’enfants, Seiberg-Witten curves and conformal blocks
Keyword(s):
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 $$ \mathcal{N} $$ 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.
2014 ◽
Vol 51
(3)
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pp. 479-489
2014 ◽
Vol 116
(3)
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pp. 195-198
2019 ◽
Vol 34
(23)
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pp. 1930011
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2020 ◽
1994 ◽
pp. 47-78
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