Higher-Derivative Gravity and the AdS/CFT Correspondence

TL;DR

This paper develops a formalism for the AdS/CFT correspondence in higher-derivative gravity, deriving a Hamilton-Jacobi-like equation and calculating Weyl anomalies, confirming consistency with N=2 superconformal field theory.

Contribution

It introduces a new formalism for boundary generating functionals in higher-derivative gravity and derives a unique Hamilton-Jacobi-like equation for the AdS/CFT correspondence.

Findings

Derived a Hamilton-Jacobi-like equation for the generating functional.

Developed an algorithm to calculate Weyl anomalies.

Confirmed the Weyl anomaly matches the field theory prediction.

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.