Amoebas and Instantons

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dc.creatorMaeda, Takashi
dc.creatorNakatsu, Toshio
dc.date2006-01-31
dc.date2006-02-27
dc.date.accessioned2026-07-07T10:45:49Z
dc.date.available2026-07-07T10:45:49Z
dc.descriptionWe study a statistical model of random plane partitions. The statistical model has interpretations as five-dimensional $\mathcal{N}=1$ supersymmetric SU(N) Yang-Mills on $\mathbb{R}^4\times S^1$ and as Kähler gravity on local SU(N) geometry. At the thermodynamic limit a typical plane partition called the limit shape dominates in the statistical model. The limit shape is linked with a hyperelliptic curve, which is a five-dimensional version of the SU(N) Seiberg-Witten curve. Amoebas and the Ronkin functions play intermediary roles between the limit shape and the hyperelliptic curve. In particular, the Ronkin function realizes an integration of thermodynamical density of the main diagonal partitions, along one-dimensional slice of it and thereby is interpreted as the counting function of gauge instantons. The radius of $S^1$ can be identified with the inverse temperature of the statistical model. The large radius limit of the five-dimensional Yang-Mills is the low temperature limit of the statistical model, where the statistical model is frozen to a ground state that is associated with the local SU(N) geometry. We also show that the low temperature limit corresponds to a certain degeneration of amoebas and the Ronkin functions known as tropical geometry.
dc.description58 pages, 28 figures, references added
dc.identifierhttps://arxiv.org/abs/hep-th/0601233
dc.identifierhttp://arxiv.org/abs/hep-th/0601233
dc.identifierInt.J.Mod.Phys.A22:937-984,2007
dc.identifierdoi:10.1142/S0217751X07034970
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/183034
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.titleAmoebas and Instantons
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