Weyl Transformation and Scalar Product

[Alamino]

I was reading about Weyl Transformations in Polchinski's book and I have a little doubt: Is it correct to say that under a Weyl transformation the scalars are invariant, i.e., that a weyl transformation preserves the scalar product?

[selfAdjoint]

Hmm, the Weyl transformation says that if you multiply the metric tensor \gamma_{(\tau,\sigma)} on the world sheet by the exponential of an arbitrary world sheet function, while keeping the X potentials the same, the metric doesn't change. Basically the transformed metric defines the same spacetime embedding as the original, WT being a degree of freedom in the derivation of the Polyakov action from the Nambu-Goto action. So I would say, yes, the scalar product is preserved by WT, and so are all the other tensor operations on the world sheet.