# One-loop tests of supersymmetric gauge theories on spheres

## TL;DR

This paper verifies that the recently proposed formulas for supersymmetric partition functions on spheres align with known flat space limits in various dimensions, supporting their validity across different supersymmetric gauge theories.

## Contribution

It demonstrates the consistency of conjectured sphere partition functions with flat space limits in multiple dimensions, including 6, 8, and 9-dimensional supersymmetric theories.

## Key findings

- Partition functions match flat space limits in 6D, 8D, and 9D.
- Supports the validity of the conjectured perturbative formulas.
- Provides evidence for the universality of the sphere partition function approach.

## Abstract

We show that a recently conjectured form for perturbative supersymmetric partition functions on spheres of general dimension $d$ is consistent with the flat space limit of 6-dimensional $\mathcal{N}=1$ super Yang-Mills. We also show that the partition functions for $\mathcal{N}=1$ 8- and 9-dimensional theories are consistent with their known flat space limits.