Large-N reduction for N=2 quiver Chern-Simons theories on S^3 and localization in matrix models

TL;DR

This paper demonstrates a novel large-N reduction for N=2 quiver Chern-Simons theories on S^3 by reducing to matrix models, and confirms the equivalence through localization and exact calculations.

Contribution

It introduces a new large-N reduction on curved space S^3 and verifies the equivalence with the original theory via localization and exact results.

Findings

Exact agreement of free energy with original theory on S^3 in large-N limit

Successful localization of reduced matrix model

Validation of large-N reduction on curved space

Abstract

We study reduced matrix models obtained by the dimensional reduction of 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.