Consistency relations and conservation of ζ in holographic inflation

It is well known that, in single clock inflation, the curvature perturbation zeta is constant in time on superhorizon scales. In the standard bulk description this follows quite simply from the local conservation of the energy momentum tensor in the bulk. On the other hand, in a holographic description, the constancy of the curvature perturbation must be related to the properties of the RG flow in the boundary theory. Here, we show that, in single clock holographic inflation, the time independence of correlators of zeta follows from the absence of the anomolous dimension of the energy momentum tensor in the boundary theory, and from the so-called consistency relations for vertex functions with a soft leg.