Children's Drawings From Seiberg-Witten Curves

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dc.creatorAshok, Sujay K.
dc.creatorCachazo, Freddy
dc.creatorDell'Aquila, Eleonora
dc.date2006-11-07
dc.date.accessioned2026-07-07T07:32:13Z
dc.date.available2026-07-07T07:32:13Z
dc.descriptionWe consider N=2 supersymmetric gauge theories perturbed by tree level superpotential terms near isolated singular points in the Coulomb moduli space. We identify the Seiberg-Witten curve at these points with polynomial equations used to construct what Grothendieck called "dessins d'enfants" or "children's drawings" on the Riemann sphere. From a mathematical point of view, the dessins are important because the absolute Galois group Gal(\bar{Q}/Q) acts faithfully on them. We argue that the relation between the dessins and Seiberg-Witten theory is useful because gauge theory criteria used to distinguish branches of N=1 vacua can lead to mathematical invariants that help to distinguish dessins belonging to different Galois orbits. For instance, we show that the confinement index defined in hep-th/0301006 is a Galois invariant. We further make some conjectures on the relation between Grothendieck's programme of classifying dessins into Galois orbits and the physics problem of classifying phases of N=1 gauge theories.
dc.description68 pages, 25 figures
dc.identifierhttps://arxiv.org/abs/hep-th/0611082
dc.identifierhttp://arxiv.org/abs/hep-th/0611082
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/119036
dc.subjectHigh Energy Physics - Theory
dc.titleChildren's Drawings From Seiberg-Witten Curves
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