Dessins d'Enfants in $\mathcal{N}=2$ Generalised Quiver Theories

Abstract

We study Grothendieck's dessins d'enfants in the context of the $\mathcal{N}=2$ supersymmetric gauge theories in $\left(3+1\right)$ dimensions with product $SU\left(2\right)$ gauge groups which have recently been considered by Gaiotto et al. We identify the precise context in which dessins arise in these theories: they are the so-called ribbon graphs of such theories at certain isolated points in the Coulomb branch of the moduli space. With this point in mind, we highlight connections to other work on trivalent dessins, gauge theories, and the modular group.

44 pages, 8 figures. v2: Minor corrections made throughout the text. Matches published version. Background discussion of BPS quivers based upon arXiv:1109.4941

References in corpus (2)

• Tri-vertices and SU(2)'s
• Strebel Differentials With Integral Lengths And Argyres-Douglas Singularities

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