Supersymmetric dyonic black holes of IIA string on Six Torus

A class of four-dimensional static supersymmetric black hole solutions of effective supergravity Lagrangian of IIA superstring compactified on $T^6$ is constructed by explicitly solving Killing spinor equations (KSEs). These solutions are dyonic black holes parametrized by four charges, with dilaton and diagonal internal metric components as the only non-zero scalar fields, and preserve $1 \over 8$ of $N=8$ supersymmetry. The KSEs with only Neveu-Schwarz-Neveu-Schwarz charges relate spinors with opposite chirality from ten-dimensional view point, and have identical structures with KSEs of toroidally compactified heterotic string. We also find a solution with four Ramond-Ramond charges which is U-dual to the solution with four Neveu-Schwarz-Neveu-Schwarz charges, and corresponds to the intersecting D-brane configuration with two 2-branes and two 4-branes. A configuration with both Neveu-Schwarz-Neveu-Schwarz charges and Ramond-Ramond charges is also found. We show that the configurations T-dual to the above solutions are also solutions of the KSEs. The patterns of supersymmetry breaking are studied in detail.