Noncritical Einstein-Weyl Gravity and the AdS/CFT Correspondence

TL;DR

This paper demonstrates that under certain conditions, four-dimensional Einstein-Weyl gravity and supergravity are effectively equivalent to Einstein gravity and AdS supergravity, allowing easier computation of dual CFT correlation functions.

Contribution

It shows the effective equivalence of Einstein-Weyl gravity and supergravity to Einstein gravity and supergravity at both quadratic and nonlinear levels in AdS spacetime.

Findings

Effective equivalence at quadratic level

Promotion to full nonlinear equivalence

Correlation functions match those of Einstein gravity

Abstract

We explore four-dimensional Einstein-Weyl gravity and supergravity on anti-de Sitter spacetime. For a specific range of the coupling with appropriate boundary conditions, we show the effective equivalence of the theory with Einstein gravity and AdS supergravity at the quadratic Lagrangian level. Furthermore we show that these equivalences can be promoted to the full nonlinear level. We also show that the similar behavior holds for the generalized Gibbons-Hawking terms. From this we find that the correlation functions in the dual conformal field theory of Einstein-Weyl gravity and supergravity can be readily read off from corresponding ones from Einstein gravity and AdS supergravity. We also give comments on some issues in critical gravity and supergravity as well as conformal gravity and supergravity.