| Abstract: | Dimensional reduction is a method to study QFTs, producing a family of theories all originating from a parent theory sitting in a higher number of dimensions. Partition functions of theories placed on compact manifolds can serve as a tool to test dimensional reductions. We are interested in T^2 x S^2 partition functions with flux on both the sphere and the torus, which requires N=2 supersymmetry. We compute the partition function for the free hypermultiplet, and test our results with the reduction of a free theory from 6D. We further compute the T^2 x S^2 partition functions of certain N=1 quiver gauge theories, motivated by their possible connection to N=4 Super Yang-Mills on the same background. |