Non-relativistic AdS/CFT and Aging/Gravity Duality

TL;DR

This work links aging phenomena in non-equilibrium systems to a gravity dual by exploiting the Schrödinger symmetry that governs $z=2$ dynamics. By embedding the Schrödinger group into the conformal group and employing a non-relativistic AdS/CFT background, the authors formulate a holographic dictionary that maps NRCFT correlators to bulk field dynamics, yielding explicit two-point functions that align with aging scaling forms. The framework naturally extends to $z\neq 2$ through the generalized geometry, offering a route to classify universality classes and compute critical indexes via classical gravity, with the promise of a full string-theoretic treatment. The approach paves the way for incorporating non-equilibrium statistical physics into holographic methods and suggests rich future directions, including higher-point functions and disordered systems.

Abstract

We point out that the recent discussion of non-relativistic AdS/CFT correspondence has a direct application in non-equilibrium statistical physics, the fact which has not been emphasized in the recent literature on the subject. In particular, we propose a duality between aging in systems far from equilibrium characterized by the dynamical exponent $z=2$ and gravity in a specific background. The key ingredient in our proposal is the recent geometric realization of the Schrödinger group. We also discuss the relevance of the proposed correspondence for the more general aging phenomena in systems where the value of the dynamical exponent is different from 2.