Causality in AdS/CFT and Lovelock theory

TL;DR

This work analyzes how causality constraints in the AdS/CFT framework restrict higher-curvature Lovelock corrections in arbitrary dimensions, focusing on cubic Lovelock gravity. It establishes two equivalent analytic approaches—black-hole perturbations and graviton–shock wave scattering—whose resulting bounds on the Lovelock couplings agree and define allowed regions in coupling space. The analysis yields explicit polynomial constraints on the vacuum structure Υ[Λ] and demonstrates how the allowed region evolves with spacetime dimension, with implications for the shear-viscosity-to-entropy ratio η/s and potential vacuum instabilities. The results elucidate how higher-curvature corrections modify holographic transport and stability while indicating deeper connections to conformal collider bounds and potential string-theory embeddings.

Abstract

We explore the constraints imposed on higher curvature corrections of the Lovelock type due to causality restrictions in the boundary of asymptotically AdS space-time. In the framework of AdS/CFT, this is related to positivity of the energy constraints that arise in conformal collider physics. We present explicit analytic results that fully address these issues for cubic Lovelock gravity in arbitrary dimensions and give the formal analytic results that comprehend general Lovelock theory. The computations can be performed in two ways, both by considering a thermal setup in a black hole background and by studying the scattering of gravitons with a shock wave in AdS. We show that both computations coincide in Lovelock theory. The different helicities, as expected, provide the boundaries defining the region of allowed couplings. We generalize these results to arbitrary higher dimensions and discuss their consequences on the shear viscosity to energy density ratio of CFT plasmas, the possible existence of Boulware-Deser instabilities in Lovelock theory and the extent to which the AdS/CFT correspondence might be valid for arbitrary dimensions.