A Novel Large-N Reduction on S^3: Demonstration in Chern-Simons Theory

TL;DR

This paper demonstrates a new large-N reduction method for Chern-Simons theory on S^3, showing that a reduced matrix model can reproduce key observables of the original theory in the planar limit.

Contribution

It introduces a novel large-N reduction for gauge theories on S^3 using a reduced model expanded around fuzzy sphere backgrounds.

Findings

Reduced model reproduces free energy of CS theory on S^3

Vacuum expectation value of unknot Wilson loop matches in the reduced model

Demonstrates equivalence in the planar limit

Abstract

We show that the planar Chern-Simons (CS) theory on S^3 can be described by its dimensionally reduced model. This description of CS theory can be regarded as a novel large-N reduction for gauge theories on S^3. We find that if one expands the reduced model around a particular background consisting of multiple fuzzy spheres, the reduced model becomes equivalent to CS theory on S^3 in the planar limit. In fact, we show that the free energy and the vacuum expectation value of unknot Wilson loop in CS theory are reproduced by the reduced model in the large-N limit.