The squashed fuzzy sphere, fuzzy strings and the Landau problem

TL;DR

This paper explores the squashed fuzzy sphere as a model for noncommutative field theory, illustrating string-like excitations and their classical dynamics related to the Landau problem.

Contribution

It introduces the squashed fuzzy sphere and demonstrates how string linking sheets emerge from fuzzy spherical harmonics, connecting noncommutative geometry with string dynamics.

Findings

Strings linking sheets are described by fuzzy spherical harmonics.

Large N limit reproduces Landau problem dynamics.

Matrix-model Laplacian matches semi-classical string behavior.

Abstract

We discuss the squashed fuzzy sphere, which is a projection of the fuzzy sphere onto the equatorial plane, and use it to illustrate the stringy aspects of noncommutative field theory. We elaborate explicitly how strings linking its two coincident sheets arise in terms of fuzzy spherical harmonics. In the large N limit, the matrix-model Laplacian is shown to correctly reproduce the semi-classical dynamics of these charged strings, as given by the Landau problem.