Can we live on a D-brane? -- Effective theory on a self-gravitating D-brane --

We consider a D-brane coupled with gravity in type IIB supergravity on S^5 and derive the effective theory on the D-brane in two different ways, that is, holographic and geometrical projection methods. We find that the effective equations on the brane obtained by these methods coincide. The theory on the D-brane described by the Born-Infeld action is not like Einstein-Maxwell theory in the lower order of the gradient expansion, i.e., the Maxwell field does not appear in the theory. Thus the careful analysis and statement for cosmology on self-gravitating D-brane should be demanded in realistic models.