Supersymmetry, Spectrum and Fate of D0-Dp Systems with B-field

It has been shown that D0-D$p$ $(p=2, 4, 6, 8)$ systems can be BPS in the presence of $B$-field even if they are not otherwise. We review the number of remaining supersymmetries, the open string ground state spectrum and the construction of the D0-D$p$ systems as solitonic solutions in the noncommutative super Yang-Mills theory. We derive the complete mass spectrum of the fluctuations to discuss the stability of the systems. The results are found to agree with the analysis in the string picture. In particular, we show that supersymmetry is enhanced in D0-D8 depending on the $B$-fields and it is consistent with the degeneracy of mass spectrum. We also derive potentials and discuss their implications for these systems.