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

TL;DR

This paper explores the connection between five-dimensional supersymmetric Yang-Mills theories and random plane partitions, revealing their factorization, relation to topological strings, and the role of ground partitions in perturbative regimes.

Contribution

It introduces a novel interpretation of random plane partitions as q-deformed partitions related to 5D Yang-Mills and topological string amplitudes, including exact partition functions and instanton effects.

Findings

Random plane partitions are factorizable as q-deformed partitions.

Ground partitions describe the perturbative regime of the gauge theories.

Partition functions include contributions from gauge instantons.

Abstract

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.