D-brane Solutions in Non-Commutative Gauge Theory on Fuzzy Sphere

TL;DR

This paper explores D-brane solutions in non-commutative gauge theory on a fuzzy sphere, identifying unstable solitons representing D0-branes and analyzing their stability, energy, and fluctuation spectra.

Contribution

It identifies and analyzes unstable D-brane soliton solutions in non-commutative gauge theory on a fuzzy sphere, extending flat space results to curved backgrounds.

Findings

Confirmed D0-brane interpretation via binding energy comparison

Found instability when D0-brane is near D2-brane

Computed the mass spectrum of 0-2 fluctuations

Abstract

Non-commutative gauge theory on fuzzy sphere was obtained by Alekseev et al. as describing the low energy dynamics of a spherical D2-brane in S^3 with the background b-field. We identify a subset of solutions of this theory which are analogs of ``unstable'' solitons on a non-commutative flat D2-brane found by Gopakumar et al. Analogously to the flat case, these solutions have the interpretation as describing D0-branes ``not yet dissolved'' by the D2-brane. We confirm this interpretation by showing the precise agreement of the binding energy computed in the non-commutative and ordinary Born-Infeld descriptions. We then study stability of the solution describing a single D0-brane off a D2-brane. Similarly to the flat case, we find an instability when the D0-brane is located close to the D2-brane. We furthermore obtain the complete mass spectrum of 0-2 fluctuations, which thus gives a prediction for the low energy spectrum of the 0-2 CFT in S^3. We also discuss in detail how the instability to a formation of the fuzzy sphere modifies the usual Higgs mechanism for small separation between the branes.