Understanding Heavy and Light Quark Brownian Motion from AdS/CFT: Analytical Analysis of Open String Evolution in the Bulk
Year: 2020
Type: preprint
Abstract: A revised, consistent, pedagogical approach to studying the motion of heavy and light probe quarks in a thermal plasma using the AdS/CFT correspondence is explored. Two cases are considered: external heavy or light quarks undergoing Brownian motion in the plasma, and an external heavy quark moving through the field theory plasma with a constant velocity.
In the bulk theory, the dual description of these probe quarks are realised as test strings in an asymptotically anti-de Sitter-Schwarzschild background. An on-mass-shell, external heavy quark is modelled as an open string attached at the AdS boundary and hanging towards the horizon. In juxtaposition, an off-mass-shell, external light quark is modelled as an open string, initially stretched between the AdS boundary and just above the horizon, whose AdS boundary endpoint is released to fall at the local speed of light. In both cases, the Schwarzschild black hole excites the modes on the string -- resulting in the string's boundary (stationary or falling) endpoint enduring irregular motion. This corresponds respectively to the heavy or light probe quark in the gauge theory undergoing Brownian motion. For both cases, the mean-squared transverse displacement of the string's boundary endpoint, $s^2(t;d)$ (equivalent to the mean-squared displacement travelled by the external quark in the thermal plasma) is computed. In the early time limit, the behaviour is found to be ballistic $s^2(t;d) \sim t^2$, while the late time dynamics are diffusive $s^2(t;d) = 2 D(d)\, t$. The diffusion coefficient $D(d)$ is extricated for both the heavy and light quark's test strings; first in AdS$_3$-Schwarzschild and then generalised to AdS$_d$-Schwarzschild.
Source: arXiv (Cornell University)
Author: Alexes Mes
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3081068719