We examine the supersymmetry of classical $D$-brane and $M$-brane configurations and explain the dependence of Killing spinors on coordinates. We find that one-half supersymmetry is broken in the bulk and that supersymmetry near the $D$-brane horizon is restored for $p<~3$, for solutions in the stringy frame, but only for $p=3\mathrm{}$ in the ten-dimensional canonical frame. We study the enhancement for the case of four intersecting $D$-3-branes in ten dimensions and the implication of this for the size of the infinite throat of the near horizon geometry in noncompactified theory. We find some indications of universality of near horizon geometries of various intersecting brane configurations.

• Received 8 May 1997

DOI:https://doi.org/10.1103/PhysRevD.56.4934