The fiducial metric comes from the gauge freedom we're afforded from the symmetries of the action, enabling us "to eliminate the integration over the metric.."

We know from a past note that the Nambu-Goto action can be written as,
\
Where I've used slightly different notation than in the past in order to align with Polchinski, and so it should be restated $...

As has been discussed, the Nambu-Goto action can be interpreted as providing the area of the worldsheet mapped by the string in spacetime. For what it is, I think this action is quite nice. There is a lot...

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