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(I'm not sure if this belongs in the BSM forum...apologies to the moderator if it belongs there.)

I'm working through Polchinski's book on string theory (volume 1) and I came cross the definition of the Nambu Goto action. I want to understand why the Nambu Goto action is proportional to the area of the world sheet. This is probably a trivial question but I'll ask anyway.

Specifically

[tex]S_{NG} = -\int_{M} d\tau d\sigma\frac{1}{2\pi\alpha'}(-\det(h_{ab}))^{1/2}[/tex]

where

[tex]h_{ab} = \partial_{a}X^\mu \partial_b X_\mu[/tex]

Thanks!

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# How is the Nambu Goto action proportional to the world sheet area?

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