TY - JOUR T1 - N=2 supersymmetric gauge theories on S^2xS^2 and Liouville Gravity JF - Journal of High Energy Physics Y1 - 2015 A1 - Aditya Bawane A1 - Giulio Bonelli A1 - Massimiliano Ronzani A1 - Alessandro Tanzini AB -

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.

VL - 2015 UR - https://doi.org/10.1007/JHEP07(2015)054 ER -