Holographic Schwinger-Keldysh field theory of SU(2) diffusion

TL;DR

This paper develops a holographic effective field theory for SU(2) charge diffusion, capturing non-Gaussian noise, nonlinear interactions, and quantum fluctuations, with a focus on the dynamical KMS symmetry in a holographic setting.

Contribution

It introduces a holographic model for SU(2) diffusion that includes non-Gaussian noise and nonlinear effects, providing a detailed quantum and thermal fluctuation analysis.

Findings

Effective action computed up to quartic order in hydrodynamical fields.

The theory incorporates non-Gaussian noise and nonlinear interactions.

Dynamical KMS symmetry has a holographic interpretation.

Abstract

We construct effective field theory for SU(2) isospin charge diffusion, based on holographic Schwinger-Keldysh contour arXiv:2008.01269. The holographic model consists of a probe SU(2) gauge field in a doubled Schwarzschild-AdS$_5$ geometry. Accurate to first order in derivative expansion, we analytically compute the effective action up to quartic order in hydrodynamical fields. The effective theory contains both non-Gaussianity for noises and nonlinear interactions between noises and dynamical variables. Moreover, the effective theory captures both thermal and quantum fluctuations, which perfectly satisfy dynamical Kubo-Martin-Schwinger (KMS) symmetry at quantum level. Interestingly, the dynamical KMS symmetry, which is crucial in formulating non-equilibrium effective field theory for a quantum many-body system, is found to have a nice holographic interpretation.