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- W2078415105 abstract "We 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(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 program of classifying dessins into Galois orbits and the physics problem of classifying phases of N = 1 gauge theories." @default.
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- W2078415105 date "2007-01-01" @default.
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- W2078415105 title "Children’s drawings from Seiberg–Witten curves" @default.
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- W2078415105 doi "https://doi.org/10.4310/cntp.2007.v1.n2.a1" @default.
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