# A Holographic Study of the $a$-theorem and RG Flow in General Quadratic Curvature Gravity

## TL;DR

This paper demonstrates the $a$-theorem for even-dimensional CFTs using holography in quadratic curvature gravity, analyzing RG flow and energy conditions near AdS boundaries.

## Contribution

It establishes the $a$-theorem holographically for higher-dimensional CFTs and explores the RG flow and energy conditions in quadratic curvature gravity.

## Key findings

- Confirmed the $a$-theorem holographically in $d\,\leq\,8$
- Derived the Wess-Zumino action from conformal symmetry breaking
- Identified conditions for monotonic RG flow in a toy model

## 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.