In sec $(3.4)$ Polchinksi says
It is easy to preserve the diff- and Poincare invariances in the quantum theory. For example, one may define the gauge fixed path integral using a Pauli-Villars regulator as is done for harmonic oscillator ... massive regulator field can be coupled to metric in diff- and Poincare invariant way. However diff- and Poincare-invariant mass term $\mu^2]\int d^2\sigma \sqrt{g}Y^\mu Y_\mu$ for regulator field is not Weyl-invariant.
My question is about the existence of a regulator which is diffeomorphic, Poincare and Weyl invariant? Adding a mass term spoils the last symmetry as mentioned above. In QED we have dimensional regulator which respects gauge invariance of $A_{\mu}$ (Schwartz $16.2$). If such a regulator exists we would have third way to derive Weyl anomaly in addition to the two given in sec$3.4$ of Polchinski.
