Gauge Theories on ALE Space and Super Liouville Correlation Functions

Understand

We present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of 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 N=2^* instanton partition function is given by the product of the character of \hat{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.