All order effective action for charge diffusion from Schwinger-Keldysh holography

Abstract

An effective action for diffusion of a conserved U(1) charge is derived to all orders in the derivative expansion within a holographic model dual to the Schwinger-Keldysh closed time path. A systematic approach to solution of the 5D Maxwell equations in a doubled Schwarzschild-AdS5 black brane geometry is developed. Constitutive relation for the stochastic charge current is shown to have a term induced by thermal fluctuations (coloured noise). All transport coefficient functions parameterising the effective action and constitutive relations are computed analytically in the hydrodynamic expansion, and then numerically for finite momenta.

Ginzburg-Landau effective action for a fluctuating holographic superconductor

“…Within this prescription, the holographic (radial) coordinate is complexified and analytically continued around the event horizon, forming a doubled Schwarzschild-AdS black hole with two conformal boundaries. In the past two years, this prescription was used to derive effective action for simple holographic systems [43][44][45][46][47][48][49], which essentially involves solving linear EOMs in doubled Schwarzschild-AdS geometry.…”

“…As an initial study, we will focus on the real-time dynamics of a fluctuating order parameter: 2 the dynamics of U(1) charge diffusion gets decoupled via switching off spatial dependence. Compared to [43][44][45][46][47][48][49], the present study goes beyond linear approximation and tests validity of the prescription [40] for nonlinear problems. The main goal is to introduce time-dependence into F GL (1.3) and put it into a non-equilibrium QFT framework.…”

“…This is in the same spirit of the treatment of [48]. Derivation of hydrodynamic effective action from AdS gravity has been nicely formulated in [52] (see also [40,49] for charge diffusion problem), based on early attempts [57][58][59]. The basis is the Gubser-Klebanov-Polyakov-Witten (GKPW) prescription [20,21] for AdS/CFT correspondence, which equals the partition functions of AdS gravity and dual CFT:…”

“…In this appendix, we provide further details on a formal derivation of boundary effective action from partially on-shell bulk solution [52]. We will closely follow [49,52], based on early attempts [57][58][59]. We would like to demonstrate that once dynamical EOMs are correctly chosen (in compatible with the chosen gauge convention), the resultant partially on-shell bulk action takes the same form.…”

An effective description of momentum diffusion in a charged plasma from holography

“…We refer the reader to the introduction of [1] (which we build on) for an overview of the salient developments. Applications of the real-time holographic techniques to diverse settings are discussed in the recent works [24][25][26][27][28].…”