= D-brane worldvolume pullbacks
{c}
{title2=$\gamma_{ab}=G_{\mu\nu}(X)\partial_aX^\mu\partial_bX^\nu,\quad B_{ab}=B_{\mu\nu}(X)\partial_aX^\mu\partial_bX^\nu$}
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 $\widetilde\Phi=\Phi(X)-\Phi_0$; otherwise use $\widetilde\Phi=\Phi(X)$ and a tension coefficient independent of that factor. These are normalization conventions for the same <Dirac-Born-Infeld action>.
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