01077nas a2200181 4500008004100000022001400041245007100055210006800126260000800194300000700202490000900209520054400218100001900762700002000781700002600801700002400827856004400851 2015 eng d a1029-847900aN=2 supersymmetric gauge theories on S^2xS^2 and Liouville Gravity0 aN2 supersymmetric gauge theories on S2xS2 and Liouville Gravity cJul a540 v20153 a
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.
1 aBawane, Aditya1 aBonelli, Giulio1 aRonzani, Massimiliano1 aTanzini, Alessandro uhttps://doi.org/10.1007/JHEP07(2015)054