= Weyl transformation
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= Weyl invariance
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= Weyl rescaling
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A <Weyl transformation> locally rescales a <metric tensor>, $g\mapsto e^{2\omega}g$, while retaining the same points and coordinates. Applied to a worldsheet metric, it leaves the embedding $X^\mu$ unchanged, and the classical <Polyakov action> is invariant under these <Weyl transformations>. Applied to a spacetime metric, a <Weyl rescaling> can relate different frame conventions, such as a string metric and an Einstein metric; the accompanying field normalizations must be transformed as well. It is not itself a coordinate transformation.
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