On the Polarization of Unstable D0-Branes into Non-Commutative Odd Spheres

TL;DR

This paper investigates how unstable D0-branes in type IIB string theory can polarize into non-commutative odd spheres, specifically fuzzy S^3, under a five-form background, revealing geometric and physical insights.

Contribution

It introduces SO(4) invariant solutions describing fuzzy S^3 configurations of unstable D0-branes, linking non-abelian Born-Infeld theory to spherical D3-branes and fuzzy geometries.

Findings

Fuzzy S^3 solutions describe polarized D0-branes.

Large N limit yields classical 3-sphere geometry.

Tachyon field relates fuzzy S^3 to fuzzy S^4 geometry.

Abstract

We consider the polarization of unstable type IIB D0-branes in the presence of a background five-form field strength. This phenomenon is studied from the point of view of the leading terms in the non-abelian Born Infeld action of the unstable D0-branes. The equations have SO(4) invariant solutions describing a non-commutative 3-sphere, which becomes a classical 3-sphere in the large N limit. We discuss the interpretation of these solutions as spherical D3-branes. The tachyon plays a tantalizingly geometrical role in relating the fuzzy S^3 geometry to that of a fuzzy S^4.