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In solving different problems in string theory and also in brane theory, we consider this static gauge choice and I think that's due to the local symmetry(Repara. Inv. and Weyl) that we have in our world sheet. So, suppose I start with strings and with a general world sheet metric (and some doable ST metric). Once we use the local symmetries to make the world sheet flat, can we still use them to make the static gauge choice? How do we do it then?

Similarly for D branes we also use the static gauge choice ..right? But I guess that's just using the R.I. I don't have any problem in convincing me in this case as I don't have Weyl here so I can't use the local symmetries to make the world volume flat. Anyway, please help me out with my misunderstandings. Thanks.

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I won't post this as a full answer but the static gauge, $\sigma_i=X_i$ for a subset of coordinates, is only helpful if the brane (or string) almost lies in the plane where all the remaining coordinates $X$ vanish - the fluctuations in those transverse dimensions are small. Then the induced metric remains flat (if in flat spacetime). I don't think it's a good idea to use the static gauge for perturbative fundamental strings. Of course, the static gauge fixes the reparametrization ambiguities completely. The Weyl sym. is independent: it rescales the auxiliary world sheet metric tensor. – Luboš Motl Feb 23 '11 at 6:59
Thanks for your reply. So, in anyway, if I have a problem with some general world sheet metric and I have made it flat by R.I and Weyl, I should not be able to make the static gauge choice further..right? – user1349 Feb 23 '11 at 14:20
If you get some time, can you please also briefly help me out with my other question, which I posted just before this one? – user1349 Feb 23 '11 at 14:25

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