Article Dans Une Revue Communications in Mathematical Physics Année : 2025

Reflexions on Mahler: Dessins, Modularity and Gauge Theories

Yang-Hui He
  • Fonction : Auteur
Ali Zahabi
  • Fonction : Auteur

Résumé

We provide a unified framework of Mahler measure, dessins d'enfants, and gauge theory. With certain physically motivated Newton polynomials from reflexive polygons, the Mahler measure and the dessin are in one-to-one correspondence. From the Mahler measure, one can construct a Hauptmodul for a congruence subgroup of the modular group, which contains the subgroup associated to the dessin. In brane tilings and quiver gauge theories, the modular Mahler flow gives a natural resolution of the inequivalence amongst the three different complex structures $\tau_{R,G,B}$. We also study how, in F-theory, 7-branes and their monodromies arise in the context of dessins. Moreover, we give a dictionary on how Mahler measure generates Gromov-Witten invariants.

Dates et versions

hal-03437028 , version 1 (19-11-2021)

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Citer

Jiakang Bao, Yang-Hui He, Ali Zahabi. Reflexions on Mahler: Dessins, Modularity and Gauge Theories. Communications in Mathematical Physics, 2025, 406 (3), pp.54. ⟨10.1007/s00220-024-05183-4⟩. ⟨hal-03437028⟩

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