Aging Logarithmic Galilean Field Theories

TL;DR

This paper uses gauge/gravity duality to analytically compute correlation functions in aging logarithmic Galilean field theories, revealing how growth exponents depend on scaling dimensions and aging parameters across various dimensions.

Contribution

It introduces a holographic framework for aging Galilean field theories with logarithmic extensions, analyzing correlation functions and growth exponents in general dimensions and dynamical exponents.

Findings

Correlation functions depend on aging parameters and scaling dimensions.

Growth exponents are controlled by different parameters at early and late times.

The results connect to field theoretical growth models like Kim-Kosterlitz.

Abstract

We analytically compute correlation and response functions of scalar operators for the systems with Galilean and corresponding aging symmetries for general spatial dimensions $d$ and dynamical exponent $z$, along with their logarithmic and logarithmic squared extensions, using the gauge/gravity duality. These non-conformal extensions of the aging geometry are marked by two dimensionful parameters, eigenvalue $\mathcal M$ of an internal coordinate and aging parameter $\alpha$. We further perform systematic investigations on two-time response functions for general $d$ and $z$, and identify the growth exponent as a function of the scaling dimensions $\Delta$ of the dual field theory operators and aging parameter $\alpha$ in our theory. The initial growth exponent is only controlled by $\Delta$, while its late time behavior by $\alpha$ as well as $\Delta$. These behaviors are separated by a time scale order of the waiting time. We attempt to make contact our results with some field theoretical growth models, such as Kim-Kosterlitz model at higher number of spatial dimensions $d$.