D-brane worldvolume pullbacks (${\gamma }_{ab}=G_{\mu \nu }(X){\partial }_a{X}^{\mu }{\partial }_b{X}^{\nu },B_{ab}=B_{\mu \nu }(X){\partial }_a{X}^{\mu }{\partial }_b{X}^{\nu }$)

The brane embedding pulls the spacetime metric and two-form back to the worldvolume. The dilaton is evaluated at that embedding. If the quoted tension includes the constant-background factor $e^{-{\Phi }_0}$, use $\tilde{\Phi }=\Phi (X)-{\Phi }_0$; otherwise use $\tilde{\Phi }=\Phi (X)$ and a tension coefficient independent of that factor. These are normalization conventions for the same Dirac-Born-Infeld action.