A Holographic Study of the \(a\)-theorem and RG Flow in General Quadratic Curvature Gravity

Abstract

We use the holographic language to show the existence of the \(a\)-theorem for even dimensional CFTs, dual to the AdS space in general quadratic curvature gravity. We find the Wess-Zumino action which is originated from the spontaneous breaking of the conformal symmetry in \(d\leq 8\), by using a radial cut-off near the AdS boundary. We also study the RG flow and (average) null energy condition in the space of the couplings of theory. In a simple toy model, we find the regions where this holographic RG flow has a monotonic decreasing behavior.