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Based on the construction by Hosomichi, Seong and Terashima we consider N=1supersymmetric 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 withdeformation parameter r and this deformation preserves 8 supercharges. Wecalculate 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 amatrix model. We perform the calculation using localization techniques. We alsoargue that in the large N-limit of this deformed 5D Yang-Mills theory thismatrix model provides the leading contribution to the partition function andthe rest is exponentially suppressed.

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