Aging Logarithmic Galilean Field Theories

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 $α$. 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 $Δ$ of the dual field theory operators and aging parameter $α$ in our theory. The initial growth exponent is only controlled by $Δ$, while its late time behavior by $α$ as well as $Δ$. 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 $d$.

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