Cosmological constant and gravitational theory on a D-brane

In a toy model we derive the gravitational equation on a self-gravitating curved D-brane. The effective theory on the brane is drastically changed from the ordinal Einstein equation. The net cosmological constant on the brane depends on a tuning between the brane tension and the brane charges. Moreover, the nonzero matter stress tensor exists if the net cosmological constant is not zero. This fact indicates a direct connection between matter on the brane and dark energy.