Partition Function of $N=2$ Gauge Theories on a Squashed $S^4$ with $SU(2)\times U(1)$ Isometry

Alejandro Cabo-Bizet; Edi Gava; V. I. Giraldo-Rivera; M. Nouman Muteeb; K. S. Narain

doi:10.1016/j.nuclphysb.2015.07.029

Partition Function of $N=2$ Gauge Theories on a Squashed $S^4$ with $SU(2)\times U(1)$ Isometry

High Energy Physics - Theory 2015-12-09 v3

Authors: Alejandro Cabo-Bizet , Edi Gava , V. I. Giraldo-Rivera , M. Nouman Muteeb , K. S. Narain

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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.

Keywords

n=2 supersymmetry gauge theories partition function squashed sphere localization technique su(2) x u(1) isometry supergravity background

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@article{arxiv.1412.6826,
  title  = {Partition Function of $N=2$ Gauge Theories on a Squashed $S^4$ with $SU(2)\times U(1)$ Isometry},
  author = {Alejandro Cabo-Bizet and Edi Gava and V. I. Giraldo-Rivera and M. Nouman Muteeb and K. S. Narain},
  journal= {arXiv preprint arXiv:1412.6826},
  year   = {2015}
}

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version to appear in Nuclear Physics B

Partition Function of $N=2$ Gauge Theories on a Squashed $S^4$ with $SU(2)\times U(1)$ Isometry

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