I have a question in reading Polchinski's string theory volume 1.

p12-p13

Given the Polyakov action
$S_P[X,\gamma]= - \frac{1}{4 \pi \alpha'} \int_M d \tau d \sigma (-\gamma)^{1/2} \gamma^{ab} \partial_a X^{\mu} \partial_b X_{\mu}$ (1.2.13),

how to show it has a Weyl invariance

$\gamma'_{ab}(\tau,\sigma) = \exp (2\omega(\tau,\sigma)) \gamma_{ab} (\tau,\sigma)$?

Because both $ (-\gamma)^{1/2} $ and $\gamma^{ab}$ give a factor $\exp(2\omega(\tau,\sigma))$, they do not cancel each other

Thank you very much in advance

This post imported from StackExchange Physics at 2014-06-29 15:46 (UCT), posted by SE-user user26143