Higher-Derivative Gravity and the AdS/CFT Correspondence

TL;DR

The paper extends the AdS/CFT correspondence to higher-derivative gravity by formulating a holographic framework in which the boundary generating functional $oldsymbol{ abla}$? The central idea is to fix the reduced classical action as a functional of boundary data, determined via a Hamilton-Jacobi-like flow equation. The authors develop a method to handle higher-derivative Lagrangians, apply it to gravity with curvature-squared terms, and show that the resulting Weyl anomaly reproduces the known $1/N$ corrections for a four-dimensional ${ m N}=2$ SCFT, consistent with prior holographic results. They also discuss a holographic RG interpretation of the Neumann boundary conditions, and outline how these techniques could illuminate holography beyond the classical gravity limit.

Abstract

We investigate the AdS/CFT correspondence for higher-derivative gravity systems, and develop a formalism in which the generating functional of the boundary field theory is given as a functional that depends only on the boundary values of bulk fields. We also derive a Hamilton-Jacobi-like equation that uniquely determines the generating functional, and give an algorithm calculating the Weyl anomaly. Using the expected duality between a higher-derivative gravity system and N=2 superconformal field theory in four dimensions, we demonstrate that the resulting Weyl anomaly is consistent with the field theoretic one.