On Higher Dimensional Fuzzy Spherical Branes

TL;DR

This paper explores the matrix descriptions of higher-dimensional fuzzy spherical branes, revealing their composition from lower-dimensional branes and the role of dielectric effects in their structure.

Contribution

It provides a detailed analysis of the structure of higher-dimensional fuzzy spheres, showing their composition from multiple lower-dimensional branes and connecting algebraic contraction to physical interpretations.

Findings

Fuzzy 2k-spheres are composed of n^{k(k-1)/2} spherical D(2k-1)-branes.

Each point on a fuzzy 2k-sphere contains a fuzzy 2(k-1)-sphere.

The dielectric effect explains the relationship between different viewpoints of these branes.

Abstract

Matrix descriptions of higher dimensional spherical branes are investigated. It is known that a fuzzy 2k-sphere is described by the coset space SO(2k+1)/U(k) and has some extra dimensions. It is shown that a fuzzy 2k-sphere is comprised of n^{\frac{k(k-1)}{2}} spherical D(2k-1)-branes and has a fuzzy 2(k-1)-sphere at each point. We can understand the relationship between these two viewpoints by the dielectric effect. Contraction of the algebra is also discussed.