Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed $S^3$ with $SU(2)\times U(1)$ Isometry

Abstract

Localization of supersymmetric $\mathcal{N}=2$ Chern-Simons-Matter theory on a squashed $S^3$ with $SU(2)\times U(1)$ isometry has been studied by different groups of authors. In this paper, we localize the theory on a squashed $S^3$ with $SU(2)\times U(1)$ isometry and a class of complex background. We see that certain kinds of shifts of the background gauge fields are crucial in obtaining nontrivial results, and the previously found results on this manifold can be incorporated in our results as special limits.

45 pages, Appendix D and some references added, typos corrected

References in corpus (6)

• Notes on SUSY Gauge Theories on Three-Sphere
• Supersymmetric Gauge Theories on the Five-Sphere
• N = 8 Superconformal Chern--Simons Theories
• Localization on Three-Manifolds
• The gravity dual of supersymmetric gauge theories on a two-parameter deformed three-sphere
• Rigid Supersymmetry on 5-dimensional Riemannian Manifolds and Contact Geometry

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