Bulk Viscosity at Extreme Limits: From Kinetic Theory to Strings

TL;DR

This paper investigates bulk viscosity in a thermal QCD model across weak to strong 't Hooft couplings, utilizing kinetic theory, lattice results, and string theory duals in type IIB and M-theory to analyze viscosity ratios and sound speed.

Contribution

It provides a comprehensive analysis of bulk viscosity in large N QCD at extreme coupling limits using both kinetic theory and string theory duals, including detailed calculations in type IIB and M-theory frameworks.

Findings

Bulk viscosity computed at weak and strong couplings.

Ratio of bulk to shear viscosity analyzed and bounded.

Sound speed and spectral functions derived and validated.

Abstract

In this paper we study bulk viscosity in a thermal QCD model with large number of colors at two extreme limits: the very weak and the very strong 't Hooft couplings. The weak coupling scenario is based on kinetic theory, and one may go to the very strong coupling dynamics via an intermediate coupling regime. Although the former has a clear description in terms of kinetic theory, the intermediate coupling regime, which uses lattice results, suffers from usual technical challenges that render an explicit determination of bulk viscosity somewhat difficult. On the other hand, the very strong 't Hooft coupling dynamics may be studied using string theories at both weak and strong string couplings using gravity duals in type IIB as well as M-theory respectively. In type IIB we provide the precise fluctuation modes of the metric in the gravity dual responsible for bulk viscosity, compute the speed of sound in the medium and analyze the ratio of the bulk to shear viscosities. In M-theory, where we uplift the type IIA mirror dual of the UV complete type IIB model, we study and compare both the bulk viscosity and the sound speed by analyzing the quasi-normal modes in the system at strong IIA string coupling. By deriving the spectral function, we show the consistency of our results both for the actual values of the parameters involved as well for the bound on the ratio of bulk to shear viscosities.