Large-Nreduction forN=2quiver Chern-Simons theories onS3and localization in matrix models

Abstract

We study reduced matrix models obtained by the dimensional reduction of $\mathcal{N}=2$ quiver Chern-Simons theories on ${S}^{3}$ to zero dimension and show that if a reduced model is expanded around a particular multiple fuzzy sphere background, it becomes equivalent to the original theory on ${S}^{3}$ in the large-$N$ limit. This is regarded as a novel large-$N$ reduction on a curved space ${S}^{3}$. We perform the localization method to the reduced model and compute the free energy and the vacuum expectation value of a BPS Wilson loop operator. In the large-$N$ limit, we find an exact agreement between these results and those in the original theory on ${S}^{3}$.