  We consider $\mathcal{N}=2$ supersymmetric gauge theories on four manifolds
admitting an isometry. Generalized Killing spinor equations are derived from
the consistency of supersymmetry algebrae and solved in the case of four
manifolds admitting a $U(1)$ isometry. This is used to explicitly compute the
supersymmetric path integral on $S^2\times S^2$ via equivariant localization.
The building blocks of the resulting partition function are shown to contain
the three point functions and the conformal blocks of Liouville Gravity.
