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 $\omega\to 0$, $T \to 0$ with $\omega / T$ held small and fixed, does not match the same at $T=0$, $\omega \to 0$. Thus the $T\to 0$ limit is not smooth for $\omega < T$. This phenomenon appears to be related to a confinement-deconfinement phase transition at $T=0$ in the field theory.