Retarded Correlators in Kinetic Theory: Branch Cuts, Poles and Hydrodynamic Onset Transitions

TL;DR

This paper investigates the collective modes of a kinetic theory for gauge theories, revealing how correlators transition from branch cuts to poles and identifying critical points where hydrodynamic modes vanish, indicating onset transitions.

Contribution

It introduces a detailed analysis of retarded correlators in kinetic theory, showing the emergence and disappearance of hydrodynamic modes and their relation to coupling and wavelength.

Findings

Correlators exhibit logarithmic branch cuts at finite coupling.

Hydrodynamic poles appear at certain wavelengths and vanish at critical points.

Onset transitions resemble phase changes in hydrodynamic behavior.

Abstract

In this work the collective modes of an effective kinetic theory description based on the Boltzmann equation in relaxation time approximation applicable to gauge theories at weak but finite coupling and low frequencies are studied. Real time retarded two-point correlators of the energy-momentum tensor and the R-charge current are calculated at finite temperature in flat space-times for large N gauge theories. It is found that the real time correlators possess logarithmic branch cuts which in the limit of large coupling disappear and give rise to non-hydrodynamic poles that are reminiscent of quasi-normal modes in black holes. In addition to branch cuts, correlators can have simple hydrodynamic poles, generalizing the concept of hydrodynamic modes to intermediate wavelength. Surprisingly, the hydrodynamic poles cease to exist for some critical value of the wavelength and coupling reminiscent of the properties of onset transitions.