Formation of Spherical D2-brane from Multiple D0-branes

TL;DR

This paper demonstrates that spherical D2-branes in the SU(2) WZW model can be described as bound states of multiple D0-branes using boundary state techniques and Wilson lines, confirming the fuzzy sphere configuration.

Contribution

It provides a boundary state construction of fuzzy sphere D-branes as bound states of D0-branes in the SU(2) WZW model, including supersymmetric extensions and stability analysis.

Findings

Boundary state with Wilson line describes fuzzy sphere D-branes.

Spherical D2-branes are bound states of D0-branes.

Non-BPS configurations are unstable due to tachyons.

Abstract

We study D-branes in SU(2) WZW model by means of the boundary state techniques. We realize the ``fuzzy sphere'' configuration of multiple D0-branes as the boundary state with the insertion of suitable Wilson line. By making use of the path-integral representation we show that this boundary state preserves the appropriate boundary conditions and leads to the Cardy state describing a spherical D2-brane under the semi-classical approximation. This result directly implies that the spherical D2-brane in SU(2) WZW model can be well described as the bound state of D0-branes. After presenting the supersymmetric extension, we also investigate the BPS and the non-BPS configurations of D-branes in the NS5 background. We demonstrate that the non-BPS configurations are actually unstable, since they always possess the open string tachyons. We further notice that the stable BPS bound state constructed by the tachyon condensation is naturally interpreted as the brane configuration of fuzzy sphere.