Abstract
We study fluctuations around equilibrium in a class of strongly interacting non-conformal plasmas using holographic techniques. In particular we calculate the quasi-normal mode spectrum of black hole backgrounds that approach to Chamblin-Reall plasmas in the IR. In a specific limit, related to the exact linear-dilaton background in string theory, we observe that the plasma approaches criticality and we obtain the quasi-normal spectrum analytically. We regulate the critical limit by gluing the IR geometry that corresponds to the non-conformal plasma to a part of AdS space-time in the UV. Near criticality, we find two sets of quasi-normal modes, related to the IR and UV parts of the geometry. In the critical limit, the quasi-normal modes accumulate to form a branch cut in the correlators of the energy-momentum tensor on the real axis of the complex frequency plane.
Highlights
Many applications of holographic duality concern systems around a critical point, where there is scale invariance
In a previous paper [4] we studied time-dependent solutions of this model corresponding to boost-invariant flow, and found that the system has a slower approach to equilibrium than in the conformal case
In the UV-completed geometry we can take the critical limit ξ → ∞ as there is no issue with the boundary conditions
Summary
Many applications of holographic duality concern systems around a critical point, where there is scale invariance. We see that when we approach the critical point, the quasinormal modes become closely spaced and their imaginary part decreases, until eventually they form a branch cut on the real axis, even as the temperature remains finite at the critical point We argue that this behavior signals a breakdown of hydrodynamics, as there are modes that decay more slowly than the hydrodynamic fluctuations. It is not clear if there is a dual theory exactly at the critical point (it has been suggested that it could correspond to an order-disorder transition in a spin model [9]). There is another set of modes, starting at a higher frequency whose imaginary part is only mildly frequency-dependent, which we associate with the slice of the AdS space
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