Localization and Large N reduction on S^3 for the Planar and M-theory limit

TL;DR

This paper demonstrates a large N reduction on S^3 for supersymmetric Chern-Simons theories, establishing equivalence with the original models in both planar and M-theory limits using localization techniques.

Contribution

It introduces a localization approach to prove large N reduction on S^3 for a broad class of supersymmetric theories, including the M-theory limit.

Findings

Large N reduction holds for supersymmetric Chern-Simons theories on S^3.

The equivalence applies to free energy and BPS Wilson loop expectations.

The reduction is valid in both planar and M-theory limits.

Abstract

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.