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.
Highlights
The prime example of a holographic theory is the maximally supersymmetric N 1⁄4 4 SYM theory, for which we have a host of results derived from the gravitational description on its properties in the hydrodynamic regime
We compare in detail the numerical and analytical approximations in order to confirm their validity; we study 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 UVcomplete situation
We studied the quasinormal modes of a strongly interacting nonconformal plasma, based on prototype holographic theories given by Chamblin-Reall blackhole solutions
Summary
The prime example of a holographic theory is the maximally supersymmetric N 1⁄4 4 SYM theory, for which we have a host of results derived from the gravitational description on its properties in the hydrodynamic regime. We have reported on the main features of the spectrum of fluctuations in [12]; in that paper we considered the sector of spin-two modes at zero momentum, derived an analytic expression for the correlator valid near the critical point, and showed that in the X → −1=2 limit the quasinormal poles condense into a branch cut on the real axis; we discussed a UV completion of the model, obtained by gluing a slice of AdS near the boundary, and showed that the QNM form two distinct sets, that can be identified respectively with modes associated to the CR geometry in the IR, and modes associated with the UV part.
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