D-brane solitons in supersymmetric sigma models

Massive $D=4,$ $N=2$ supersymmetric sigma models typically admit domain wall $(Q$-kink) solutions and string $(Q$-lump) solutions, both preserving 1/2 supersymmetry. We exhibit a new static 1/4 supersymmetric ``kink-lump'' solution in which a string ends on a wall, and show that it has an effective realization as a bion of the $D=4$ super DBI action. It is also shown to have a time-dependent Q-kink-lump generalization which reduces to the Q lump in a limit corresponding to infinite BI magnetic field. All these 1/4 supersymmetric sigma-model solitons are shown to be realized in M theory as calibrated, or ``Q calibrated,'' M5-branes in an M-monopole background.