 Weyl transformation

A Weyl transformation rescales the worldsheet metric locally, $g_{\alpha \beta }\mapsto e^{2\omega (\sigma )}{g}_{\alpha \beta }$, without changing $X^{\mu }$. The classical Polyakov action is Weyl invariant.

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.