Description:
<jats:title>A<jats:sc>bstract</jats:sc>
</jats:title><jats:p>We construct effective field theory for SU(2) isospin charge diffusion, based on holographic Schwinger-Keldysh contour [1]. The holographic model consists of a probe SU(2) gauge field in a doubled Schwarzschild-AdS<jats:sub>5</jats:sub> geometry. Accurate to first order in derivative expansion, we analytically compute the effective action up to quartic order in dynamical variables. 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.</jats:p>