Relation With Nambu-Goto Action
Writing the Euler-Lagrange equation for the metric tensor one obtains that:
Knowing also that:
One can write the variational derivative of the action:
where which leads to:
If the auxiliary worldsheet metric tensor is calculated from the equations of motion:
and substituted back to the action, it becomes the Nambu-Goto action:
However, the Polyakov action is more easily quantized because it is linear.
Read more about this topic: Polyakov Action
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