Lifshitz quasinormal modes and relaxation from holography

TL;DR

This paper investigates the relaxation dynamics of Lifshitz field theories with holographic duals by computing quasinormal modes, revealing how relaxation times depend on the dynamical exponent and boundary dimension.

Contribution

It provides a detailed analysis of Lifshitz quasinormal modes and their relation to relaxation times, including analytical results for specific parameter regimes.

Findings

For d>z+1, modes are non-overdamped at zero momentum.

For d<=z+1, the system is always overdamped.

Analytical solutions are obtained for d=z+1 at zero momentum.

Abstract

We obtain relaxation times for field theories with Lifshitz scaling and with holographic duals Einstein-Maxwell-Dilaton gravity theories. This is done by computing quasinormal modes of a bulk scalar field in the presence of Lifshitz black branes. We determine the relation between relaxation time and dynamical exponent z, for various values of boundary dimension d and operator scaling dimension. It is found that for d>z+1, at zero momenta, the modes are non-overdamped, whereas for d<=z+1 the system is always overdamped. For d=z+1 and zero momenta, we present analytical results.