Stirring Strongly Coupled Plasma

Abstract

We determine the energy it takes to move a test quark along a circle of radius L with angular frequency ω through the strongly coupled plasma of $\mathcal{N}=4$ supersymmetric Yang–Mills (SYM) theory. We find that for most values of L and ω the energy deposited by stirring the plasma in this way is governed either by the drag force acting on a test quark moving through the plasma in a straight line with speed v=L ω or by the energy radiated by a quark in circular motion in the absence of any plasma, whichever is larger. There is a continuous crossover from the drag-dominated regime (ω≲π T(1−v [superscript 2])[superscript 3/4], meaning ω≲π T and L small enough) to the radiation-dominated regime (ω≳π T(1−v [superscript 2])[superscript 3/4]). In the crossover regime we find evidence for significant destructive interference between energy loss due to drag and due to radiation as if in vacuum. The rotating quark thus serves as a model system in which the relative strength of, and interplay between, two different mechanisms of parton energy loss is accessible via a controlled classical gravity calculation. We close by speculating on the implications of our results for a quark that is moving through the plasma in a straight line while decelerating, although in this case the classical calculation breaks down at the same value of the deceleration as the one at which the radiation-dominated regime sets in.