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 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.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics