Partition function of N=2 gauge theories on a squashed S4 with SU(2)×U(1) isometry

We study N=2 supersymmetric gauge theories on a large family of squashed 4-spheres preserving SU(2)×U(1)⊂SO(4) isometry and determine the conditions under which this background is supersymmetric. We then compute the partition function of the theories by using localization technique. The results indicate that for N=2 SUSY, including both vector-multiplets and hypermultiplets, the partition function is independent of the arbitrary squashing functions as well as of the other supergravity background fields.Fil: Cabo Bizet, Alejandro. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Gava, Edi. SISSA; ItaliaFil: Giraldo Rivera, Victor Ivan. SISSA; ItaliaFil: Nouman Muteeb, M.. SISSA; ItaliaFil: Narain, K. S.. ICTP; Itali