# Why does product of Moduli and Diff x Weyl Variation vanish?

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According to equation 5.2.5 in Polchinski :-

$$\int d^2 \sigma~ \delta^{'}g_{ab} \times [-2(P_1 \delta \sigma)_{ab} +(2\delta w - \Delta \cdot \delta \sigma)g^{ab}]=0$$

The assumption here is that " Moduli correspond to variation $\delta^{'}g_{ab}$ of the metric that are orthogonal to all variations of DiffxWeyl type given by the quantity in []"

My question is that why are we imposing that orthogonality ? How can variation in the metric due to moduli be orthogonal to variation due to other Diff x Weyl ?

This post imported from StackExchange Physics at 2014-08-27 18:48 (UCT), posted by SE-user sol0invictus
asked Aug 27, 2014

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