Localization and large N reduction on [formula omitted] for the planar and M-theory limit

Abstract

We show a large N reduction on S3 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 S3 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 S3 holds also for the M-theory limit.