Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-01-31
Int.J.Mod.Phys.A22:937-984,2007
Physics
High Energy Physics
High Energy Physics - Theory
58 pages, 28 figures, references added
Scientific paper
10.1142/S0217751X07034970
We 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 K\"ahler 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.
Maeda Takashi
Nakatsu Toshio
No associations
LandOfFree
Amoebas and Instantons does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Amoebas and Instantons, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Amoebas and Instantons will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-353803