Localization of supersymmetric Chern-Simons-Matter theory on a squashed S3 with SU (2) x U (1) isometry

Localization of supersymmetric N = 2 Chern-Simons-Matter theory on a squashed S-3 with SU(2) x 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) x 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.