Three-point functions of aging dynamics and the AdS-CFT correspondence

Aging can be realized as a subalgebra of Schrödinger algebra by discarding the time-translation generator. While the two-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 three-point correlators of scalar primary operators. We find that the aging correlators are distinct from the Schrödinger correlators by more than certain dressings with time-dependent factors, as was the case with two-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 Schrödinger theory. Consequently, the aging two-point functions derived from holography look as the Schrödinger two-point functions dressed by time-dependent factors. However, since the three-point functions obtained in this Letter are not merely dressed Schrödinger 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. We also comment on various extensions of the Schrödinger and aging algebras.