5D Super Yang-Mills on $Y^{p,q}$ Sasaki-Einstein manifolds

Understand

On any simply connected Sasaki-Einstein five dimensional manifold one can construct a super Yang-Mills theory which preserves at least two supersymmetries.

• We study the special case of toric Sasaki-Einstein manifolds known as $Y^{p,q}$ manifolds.
• We use the localisation technique to compute the full perturbative part of the partition function.
• The full equivariant result is expressed in terms of certain special function which appears to be a curious generalisation of the triple sine function.