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I am reading the paper https://arxiv.org/abs/1808.07032 - "Statistical mechanics of two dimensional black hole".

And here sometimes $\widetilde{AdS}_2$ and $\widetilde{\text{SL}}(2, \mathbb{R})$ are accompanied with a tilde.

Seems like this kind of notation has certain purpose, to distinguish from $AdS_2$ and $\text{SL}(2, \mathbb{R})$ in more common sense. However, I cannot infer what is meant from the paper?

Sorry, for a stupid question, but I really would like to make clear this point

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If you scroll down to the appendix, that paper uses the notation from this review paper, which in turn defines $\widetilde{\mathrm G}$ to be the universal cover of $\mathrm G$.

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