Thermodynamics, transport and relaxation in non-conformal theories

TL;DR

This paper investigates the thermodynamics, transport properties, and relaxation dynamics of a non-conformal holographic gauge theory, revealing deviations from conformality, violations of viscosity bounds, and temperature-dependent relaxation channels.

Contribution

It provides a detailed analysis of non-conformal holographic models, including thermodynamics, viscosity ratios, and relaxation modes, highlighting novel behaviors at different temperature regimes.

Findings

Bulk viscosity over shear viscosity ratio violates Buchel's bound.

At high temperatures, pressures equilibrate before reaching the equation of state.

At low temperatures, pressures first reach equilibrium, then become equal.

Abstract

We study the equilibrium and near-equilibrium properties of a holographic five-dimensional model consisting of Einstein gravity coupled to a scalar field with a non-trivial potential. The dual four-dimensional gauge theory is not conformal and, at zero temperature, exhibits a renormalisation group flow between two different fixed points. We quantify the deviations from conformality both in terms of thermodynamic observables and in terms of the bulk viscosity of the theory. The ratio of bulk over shear viscosity violates Buchel's bound. We study relaxation of small-amplitude, homogeneous perturbations by computing the quasi-normal modes of the system at zero spatial momentum. In this approximation we identify two different relaxation channels. At high temperatures, the different pressures first become approximately equal to one another, and subsequently this average pressure evolves towards the equilibrium value dictated by the equation of state. At low temperatures, the average pressure first evolves towards the equilibrium pressure, and only later the different pressures become approximately equal to one another.