D-BRANES AND THE NONCOMMUTATIVE TORUS

We show that in certain superstring compactifications, gauge theories on noncommutative tori will naturally appear as D-brane world-volume t heories. This gives strong evidence that they are well-defined quantum theories. It also gives a physical derivation of the identification p roposed by Connes, Douglas and Schwarz of Matrix theory compactificati on on the noncommutative torus with M theory compactification with con stant background three-form tensor field.