Residual conformal transformation

After conformal gauge fixing, independent reparameterizations ${\sigma }^{+}\mapsto f({\sigma }^{+})$ and ${\sigma }^{-}\mapsto \tilde{f}({\sigma }^{-})$ remain, accompanied by a compensating Weyl transformation.

Light-cone gauge uses residual conformal transformations to make the target-space coordinate $X^{+}$ linear in worldsheet time. The Virasoro constraints then determine $X^{-}$ from the transverse fields.