Oscillating D-strings from type IIB matrix theory

We present a class of BPS solutions of the type IIB matrix theory which preserves 1/4 supersymmetry. The solutions describe $D$-string configurations with left-moving oscillations. We demonstrate that the one-loop quantum effective action of matrix theory vanishes for this solution, confirming its BPS nature. We also study the world-volume gauge theory of oscillating strings and show its connection with static $D$-strings.