Solitons for the fuzzy sphere from matrix model

TL;DR

This paper explores classical and noncommutative solitons on the fuzzy sphere derived from a matrix model, analyzing their behavior in the large N limit and the impact of coupling constants.

Contribution

It introduces a method to obtain classical solitons on the fuzzy sphere from a matrix model with two coupling constants, especially in the large N limit.

Findings

Classical solitons are derived in the large N limit.

Finite N results yield a noncommutative version of the solitons.

The development of the coupling constant λ is crucial for the classical limit.

Abstract

Recently we have introduced a matrix model depending on two coupling constants $g^2$ and $\lambda$, which contains the fuzzy sphere as a background; to obtain the classical limit $g^2$ must depend on $N$ in a precise way. In this paper we show how to obtain the classical solitons of the $N \to \infty$ limit imposing the development $\lambda = \half + \frac{\lambda_0}{N}$; as a consequence at finite $N$ one obtains a noncommutative version of the solitons for the fuzzy sphere.