Gauge Theories and Dessins d'Enfants: Beyond the Torus

Abstract

Dessin d'Enfants on elliptic curves are a powerful way of encoding doubly-periodic brane tilings, and thus, of four-dimensional supersymmetric gauge theories whose vacuum moduli space is toric, providing an interesting interplay between physics, geometry, combinatorics and number theory. We discuss and provide a partial classification of the situation in genera other than one by computing explicit Belyi pairs associated to the gauge theories. Important also is the role of the Igusa and Shioda invariants that generalise the elliptic $j$-invariant.

arXiv comment53 pages, 3 figures

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Cited by in corpus (8)

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• Sporadic and Exceptional
• A Database of Belyi Maps
• Composite Genus One Belyi Maps
• Yang-Mills Theory and the ABC Conjecture
• A generalization of cancellative dimer algebras to hyperbolic surfaces
• Cyclic contractions of dimer algebras always exist
• Reflexions on Mahler: Dessins, Modularity and Gauge Theories