= Classical equivalence of Polyakov and Nambu–Goto actions
{title2=$h_{ab}=\Omega^2\gamma_{ab}$}
Varying the independent metric in the <Polyakov action> sets the <worldsheet stress tensor> to zero. For a nondegenerate timelike embedding in two <worldsheet> dimensions, the metric is proportional to the <induced worldsheet metric>. The conformal factor cancels from the action, which becomes the <Nambu–Goto action>. This elimination is classical; the quantum measure and <worldsheet Weyl anomaly> require separate treatment.
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