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Finite temperature is introduced in the Ads Space by inserting a black hole. In the Ads-CFT correspondence, the Wilson loop is at $u \rightarrow \infty$. But the black hole horizon itself would be at $u \rightarrow u_0$, i.e. a finite u, implying that the black hole mass is finite.

For reference, let me specify the metric in 10D space as $\frac{u^2}{a^2} (-H dt^2 + dx_{||}^2) + \frac{a^2}{u^2}(\frac{du^2}{H} + d\Omega^2)$, with H = $1 - u^4/a^4$. This shows that the black hole horizon is at u = a. And the dimension u is interpreted as energy dimension.

Does this mean that the gauge particles described by the Wilson loop is heavier than the black hole, since the Wilson loop is at $u = \infty$?

Is it a mathematical jugglery to introduce finite temperature without worrying about the physical possibility?

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