Factorization of 5D super Yang-Mills on $Y^{p,q}$ spaces

Understand

We continue our study on the partition function for 5D supersymmetric Yang-Mills theory on toric Sasaki-Einstein $Y^{p,q}$ manifolds.

• Previously, using the localisation technique we have computed the perturbative part of the partition function.
• In this work we show how the perturbative part factorises into four pieces, each corresponding to the perturbative answer of the same theory on $\mathbb{R}^4 \times S^1$.
• This allows us to identify the equivariant parameters and to conjecture the full partition functions (including the instanton contributions) for $Y^{p,q}$ spaces.