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There is a standard procedure to show that for CFT's in dimension $d\geq 2$, the trace of stress tensor vanishes. I think I can't apply those steps when I only have one dimension, say time, because if we could then we can show that stress tensor trace $T_{tt}$ (which is basically it) also vanishes which may not be true always. Things are definitely different in 1D (I think metric can just be $g_{tt}$ and conformal transformation just a $t\rightarrow \lambda t$ transformation. Please correct me if I am wrong.) So, where do basically things go wrong in such derivation?

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Every 1D metric is flat (not just conformally flat as in 2D) because we can always reparametrize the only metric function smoothly to a constant. Therefore in 1D it makes no sense to talk about conformal transformations. – Marek Aug 11 '11 at 10:54
That's true. Its kind of trivial. But still non-trivial work goes on when people talk about $AdS_2/CFT_1$. – user1349 Aug 11 '11 at 14:06

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