Fluctuations in a nonconformal holographic plasma at criticality
Résumé
We continue the study initiated in [P. Betzios, U. Gürsoy, M. Järvinen, and G. Policastro, Phys. Rev. D 97, 081901 (2018).PRVDAQ2470-001010.1103/PhysRevD.97.081901] of the fluctuations of a strongly coupled nonconformal 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 quasinormal 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 Wentzel-Kramers-Brillouin approximation) the momentum dependence of the modes, in order to determine the crossover 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.