Dynamic critical phenomena in the AdS/CFT duality

TL;DR

The paper investigates dynamic critical phenomena in the AdS/CFT framework by studying black holes with a single R-charge, revealing a conserved-charge diffusion (Model B) universality across D=4,5,7 with a vanishing diffusion constant $D_R$ at the critical lines while the conductivity $\lambda$ remains finite. Using linear perturbations and Green-Kubo relations, it demonstrates critical slowing down and derives dimension-dependent static exponents $\alpha,\beta,\gamma,\delta,\nu,\eta$, together with a dynamic exponent $z=4-\eta$ (subject to potential hyperscaling caveats). Extensions to multiple dimensions show consistent qualitative behavior, connecting holographic critical dynamics to QCD-like critical points and guiding future nonlinear and interfacial studies. The work highlights how AdS/CFT can capture universal dynamic critical behavior in strongly coupled gauge theories and points to further probes of transport phenomena near criticality.

Abstract

In critical phenomena, singular behaviors arise not only for thermodynamic quantities but also for transport coefficients. We study this dynamic critical phenomenon in the AdS/CFT duality. We consider black holes with a single R-charge in various dimensions and compute the R-charge diffusion in the linear perturbations. In this case, the black holes belong to model B according to the classification of Hohenberg and Halperin.