All order effective action for charge diffusion from Schwinger-Keldysh holography
arXiv:2012.08362 · doi:10.1007/JHEP05(2021)187
Abstract
An effective action for diffusion of a conserved 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-AdS 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.
arXiv commentv1: 59 pages, 11 multi-figures; v2: 53 pages in JHEP style, refs added, one appendix added, revised the partially off-shell procedure based on bulk path integral
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