A Weyl transformation, also known as a Weyl scaling, is a type of transformation in which the metric of a space is rescaled by a smooth, positive function. It is commonly used in the context of differential geometry, theoretical physics, and especially in the study of conformal field theories and general relativity.
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A Weyl transformation locally rescales a metric tensor, , while retaining the same points and coordinates. Applied to a worldsheet metric, it leaves the embedding 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.