On the 3-point functions of Aging Dynamics and the AdS/CFT Correspondence

TL;DR

This paper derives novel 3-point correlators for Aging dynamics within the holographic framework, revealing they differ fundamentally from Schr"odinger correlators and indicating the need for a more general holographic model.

Contribution

It presents the first explicit form of 3-point functions in Aging, showing they are not just dressed Schr"odinger correlators and depend on additional variables.

Findings

Aging 3-point functions differ from Schr"odinger ones beyond simple dressings.

Holographic duals of Aging require a more general construction.

Aging correlators depend on an extra time-translation breaking variable.

Abstract

Aging can be realized as a sub-algebra of Schr\"odinger algebra by discarding the time-translation generator. While the 2-point functions of the Age algebra have been known for some time, little else was known about the higher $n$-point correlators. In this letter we present novel 3-point correlators of scalar primary operators. We find that the Aging correlators are distinct from the Schr\"odinger correlators by more than certain dressings with time-dependent factors, as was the case with 2-point functions. In the existing literature, the holographic geometry of Aging is obtained by performing certain general coordinate transformations on the holographic dual of the Schr\"odinger theory. Consequently, the Aging 2-point functions derived from holography look as the Schr\"odinger 2-point functions dressed by time-dependent factors. However, since the 3-point functions obtained in this letter are not merely dressed Schr\"odinger correlators and instead depend on an additional time-translation breaking variable, we conclude that the most general holographic realization of Aging is yet to be found.