Editing Worldsheet (section)

==== World-sheet metric ====
In order to define the [[Polyakov action]], the world-sheet is equipped with a '''world-sheet metric'''<ref name="Polchinski">{{cite book|last1=Polchinski|first1=Joseph|year=1998|title=String Theory, Volume 1: Introduction to the Bosonic string}}</ref> <math>\mathbf{g}</math>, which also has signature <math>(-, +)</math> but is independent of the induced metric.

Since [[Weyl transformation]]s are considered a redundancy of the metric structure, the world-sheet is instead considered to be equipped with a [[conformal class]] of metrics <math>[\mathbf{g}]</math>. Then <math>(\Sigma, [\mathbf{g}])</math> defines the data of a [[conformal manifold]] with signature <math>(-, +)</math>.