Fluctuations in non-conformal holographic plasma at criticality

TL;DR

This paper analyzes the fluctuation spectrum of a non-conformal holographic plasma near a critical point, revealing the coalescence of quasinormal modes into a branch cut and exploring the limits of hydrodynamic descriptions.

Contribution

It provides an extended analysis of quasinormal modes at criticality, including analytical, numerical, and approximation methods, and discusses UV completion techniques.

Findings

Quasinormal frequencies form a branch cut at criticality.

Hydrodynamic approximation validity diminishes near the critical point.

Analytical and numerical methods agree on the mode spectrum.

Abstract

We continue the study initiated in [arXiv:1708.02252] of the fluctuations of a strongly-coupled non-conformal plasma described holographically by Einstein gravity coupled to a dilaton with an exponential potential. The plasma approaches a critical point of a continuous phase transition in a specific limit, where the metric becomes a linear-dilaton background. This results to an analytic description of the quasi-normal mode spectrum, that can be extended perturbatively in the deviation away from the critical point. In the previous paper we showed that at criticality the quasinormal frequencies coalesce into a branch cut on the real axis. In this paper we give a more extended and complete discussion of these results. We compare in detail the numerical and analytical approximations in order to confirm their validity; we study (numerically and in a WKB approximation) the momentum dependence of the modes, in order to determine the cross-over scale that limits the validity of the hydrodynamic approximation, and which becomes arbitrarily low at the critical point; and we discuss in detail the procedure we use to complete the theory in the UV by gluing a slice of AdS geometry, and the extent to which it should provide a good approximation to a smooth UV-complete situation.