= Einstein-frame metric
{c}
{title2=$g^{(E)}_{ab}=e^{-4\varphi/(D-2)}g^{(s)}_{ab}$}
= Einstein frame
{c}
{synonym}
For $D>2$, rescale the <string-frame metric> by $g^{(E)}=e^{-4\varphi/(D-2)}g^{(s)}$. The <Weyl transformation> of the <Ricci scalar> makes the coefficient of the Einstein-frame Ricci term independent of the <dilaton>. Indeed $g^{(s)}=e^{4\varphi/(D-2)}g^{(E)}$ contributes factors $e^{2D\varphi/(D-2)}$ from the volume, $e^{-2\varphi}$ from the original coupling and $e^{-4\varphi/(D-2)}$ from the Ricci term; their product is one. Derivative terms supply the transformed dilaton kinetic term. The two-dimensional case is excluded from this particular rescaling.
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