Localization and Large N reduction on S³ for the Planar and M-theory limit

We show a large N reduction on S^3 in a BPS sector for a broad class of theories : N>=2 supersymmetric Chern-Simons theory with any number of adjoint and bi-fundamental chiral multiplets.We show that a localization method can be applied to the reduced model and the path integral can be written by a multi-contour integral. By taking a particular localization configuration, we also show that the large N equivalence between the original theory on S^3 and the reduced model holds for the free energy and the expectation value of BPS Wilson loops. It turns out that the large N reduction on S^3 holds also for the M-theory limit.