Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-12-30
Nucl.Phys. B715 (2005) 275-303
Physics
High Energy Physics
High Energy Physics - Theory
32 pages, 3 figures, typos corrected
Scientific paper
10.1016/j.nuclphysb.2005.02.041
A model of random plane partitions which describes five-dimensional $\mathcal{N}=1$ supersymmetric SU(N) Yang-Mills is studied. We compute the wave functions of fermions in this statistical model and investigate their thermodynamic limits or the semi-classical behaviors. These become of the WKB type at the thermodynamic limit. When the fermions are located at the main diagonal of the plane partition, their semi-classical wave functions are obtained in a universal form. We further show that by taking the four-dimensional limit the semi-classical wave functions turn to live on the Seiberg-Witten curve and that the classical action becomes precisely the integral of the Seiberg-Witten differential. When the fermions are located away from the main diagonal, the semi-classical wave functions depend on another continuous parameter. It is argued that they are related with the wave functions at the main diagonal by the renormalization group flow of the underlying gauge theory.
Maeda Takashi
Nakatsu Toshio
Takasaki Kanehisa
Tamakoshi Takeshi
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