Gauge Theories on ALE Space and Super Liouville Correlation Functions

We present a relation between ${mathcal{N}=2}$ quiver gauge theories on the ALE space ${mathcal{O}_{mathbb{P}^1}(-2)}$ and correlators of ${mathcal{N}=1}$ super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the ${mathcal{N}=2^*}$ instanton partition function is given by the product of the character of ${widehat{SU}(2)_2}$ times the super Virasoro conformal block on the torus with one puncture. Moreover, we match the perturbative gauge theory contribution with super Liouville three-point functions.