The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere

TL;DR

This paper computes the exact perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on a five-sphere using localization, revealing insights into its large N behavior and matrix model representation.

Contribution

It provides the first explicit calculation of the full perturbative partition function for 5D supersymmetric Yang-Mills with matter on a curved space, extending previous flat space results.

Findings

Partition function expressed as a matrix model depending on radius and coupling

Large N-limit dominated by the matrix model contribution

Localization technique successfully applied to 5D supersymmetric theories

Abstract

Based on the construction by Hosomichi, Seong and Terashima we consider N=1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation of the theory in flat space with deformation parameter r and this deformation preserves 8 supercharges. We calculate the full perturbative partition function as a function of r/g^2, where g is the Yang-Mills coupling, and the answer is given in terms of a matrix model. We perform the calculation using localization techniques. We also argue that in the large N-limit of this deformed 5D Yang-Mills theory this matrix model provides the leading contribution to the partition function and the rest is exponentially suppressed.