2006/01/31 by Takashi Maeda, Toshio Nakatsu · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th #math.AG
paper · pdf · doi:10.1142/s0217751x07034970
published as Int.J.Mod.Phys.A22:937-984,2007 · 58 pages, 28 figures, references added
arxiv created 2006/02/27 · openalex publication_date 2007/02/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a statistical model of random plane partitions. The statistical model has interpretations as five-dimensional [Formula: see text] supersymmetric SU (N) Yang–Mills on ℝ 4 × 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.