Five-Dimensional Supersymmetric Yang-Mills Theories and Random Plane Partitions

Research paper by Takashi Maeda, Toshio Nakatsu, Kanehisa Takasaki, Takeshi Tamakoshi

Indexed on: 09 May '05Published on: 09 May '05Published in: High Energy Physics - Theory


Five-dimensional $\mathcal{N}=1$ supersymmetric Yang-Mills theories are investigated from the viewpoint of random plane partitions. It is shown that random plane partitions are factorizable as q-deformed random partitions so that they admit the interpretations as five-dimensional Yang-Mills and as topological string amplitudes. In particular, they lead to the exact partition functions of five-dimensional $\mathcal{N}=1$ supersymmetric Yang-Mills with the Chern-Simons terms. We further show that some specific partitions, which we call the ground partitions, describe the perturbative regime of the gauge theories. We also argue their role in string theory. The gauge instantons give the deformation of the ground partition.