Formation of Spherical D2-brane from Multiple D0-branes

TL;DR

The paper demonstrates that spherical D2-branes in the SU(2) WZW model can be understood as bound states of multiple D0-branes by constructing boundary states with a Wilson line implementing fuzzy-sphere CP matrices. In the bosonic case, the large-k limit shows the D0-bound state boundary state converges to the D2 Cardy state wrapped on a conjugacy class; in the supersymmetric NS5 background, only the fuzzy-sphere D0 configuration remains BPS, while other D0 configurations harbor open-string tachyons that condense to the D2 bound state. Tachyon condensation is thus interpreted as the mechanism by which unstable D0 configurations flow to stable fuzzy-sphere D2 branes, with a consistent central-charge and mass accounting. The work connects boundary-state techniques to geometric descriptions of brane bound states and discusses extensions to N=2/N=4 SUSY and the CHS background, offering a boundary-CFT perspective on brane formation in curved backgrounds. Overall, it provides a concrete CFT realization of D2 branes as D0 bound states and elucidates stability via tachyon dynamics in NS5 geometries.

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.