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

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

2004-12-30

arxiv.org/abs/hep-th/0412327v3

JHEP 0503 (2005) 056

Physics

High Energy Physics

High Energy Physics - Theory

33 pages, 9 figures, typos corrected

Scientific paper

10.1088/1126-6708/2005/03/056

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.

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