Zero Temperature Dissipation and Holography

We use holographic techniques to study the zero-temperature limit of dissipation for a Brownian particle moving in a strongly coupled CFT at finite temperature in various space-time dimensions. The dissipative term in the boundary theory for $ω\to 0$, $T \to 0$ with $ω/ T$ held small and fixed, does not match the same at $T=0$, $ω\to 0$. Thus the $T\to 0$ limit is not smooth for $ω< T$. This phenomenon appears to be related to a confinement-deconfinement phase transition at $T=0$ in the field theory.

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