Zero Temperature Dissipation and Holography

Abstract

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.

Comments: 23 pages, 1 figure, v2 : minor improvements of the text, one figure added, accepted for publication in JHEP