Abstract
We discuss the physics of momentum diffusion in a charged plasma. Following the holographic strategy outlined in [1] we construct an open effective field theory for the low-lying modes of the conserved currents. The charged plasma is modeled holographically in terms of a Reissner-Nordström-AdSd+1 black hole. We analyze graviton and photon fluctuations about this background, decoupling in the process the long-lived momentum diffusion mode from the short-lived charged transport mode. Furthermore, as in the aforementioned reference, we argue that the dynamics of these modes are captured by a set of designer scalars in the background geometry. These scalars have their gravitational coupling modulated by an auxiliary dilaton with long-lived modes being weakly coupled near the spacetime asymptopia. Aided by these observations, we obtain the quadratic effective action that governs the fluctuating hydrodynamics of the charge current and stress tensor, reproducing in the process transport data computed previously. We also point out an interesting length scale lying between the inner and outer horizon radii of the charged black hole associated with Ohmic conductivity.
Highlights
As in the aforementioned reference, we argue that the dynamics of these modes are captured by a set of designer scalars in the background geometry
The dissipative dynamics of planar AdS black holes is encoded in their quasinormal spectrum, while the associated quantum and stochastic fluctuations are captured by Hawking quanta
We have extended the analysis of open quantum systems with long-lived modes using holography initiated in [1] to systems with multiple degrees of freedom, focusing on the dynamics of momentum diffusion in a charged plasma
Summary
The dissipative dynamics of planar AdS black holes is encoded in their quasinormal spectrum, while the associated quantum and stochastic fluctuations are captured by Hawking quanta. The trick is to not compute the generating function of the correlators (which would involve integrating out the long-lived modes leading to non-locality), but rather to parameterize the effective action in terms of the long-lived moduli fields This choice is naturally forced upon one from the bulk gravity: the gauge invariant combinations are required to be quantized with alternate (Neumann) boundary conditions to ensure that the parent gauge or gravitational perturbations satisfy the standard (Dirichlet) boundary conditions.. We will use the gravitational description to argue for a suitable parameterization of the CFT currents which decouples the Markovian and non-Markovian sectors It should become clear during the course of our discussion that such should always be possible purely in field theoretic terms (i.e., no assumptions of holographic duals). The relation between bulk and boundary observables is described in detail in appendix E, which we employ extensively in our analysis
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