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Partition Function of $N=2$ Gauge Theories on a Squashed $S^4$ with $SU(2)\times U(1)$ Isometry (1412.6826v3)
Published 21 Dec 2014 in hep-th
Abstract: We study $N=2$ supersymmetric gauge theories on a large family of squashed 4-spheres preserving $SU(2)\times U(1)\subset SO(4)$ 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.